]>
2022
25
4
87
Cauchy problem for inhomogeneous fractional nonclassical diffusion equation on the sphere
Cauchy problem for inhomogeneous fractional nonclassical diffusion equation on the sphere
en
en
Pseudo-parabolic equation on spheres have many important applications in physical
phenomena, oceanography and meteorology, geophysics. The main purpose of this paper is to prove
the existence and unique solution of the nonlinear pseudo-parabolic equation on the sphere. To
do this, we used some analysis of Fourier series associated with several evaluations of the
spherical harmonics function. Some of the upper and lower bounds of the Mittag-Lefler functions are also used. This result is one of the first studies of fractional nonclassical diffusion equation on
the sphere.
303
311
L. D.
Long
Division of Applied Mathematic
Thu Dau Mot University
Viet Nam
ledinhlong@tdmu.edu.vn
Fractional diffusion equation
Riemman-Liouville
regularity
Article.1.pdf
[
[1]
K. A. Abro, A. Atangana, Mathematical analysis of memristor through fractal‐fractional differential operators: a numerical study, Math. Methods Appl. Sci., 43 (2020), 6378-6395
##[2]
A. Atangana, A. Akgül, K. M. Owolabi, Analysis of fractal fractional differential equations, Alexandria Eng. J., 59 (2020), 1117-1134
##[3]
A. Atangana, E. Bonyah, Fractional stochastic modeling: New approach to capture more heterogeneity, Chaos, 29 (2019), 1-13
##[4]
A. Atangana, E. F. D. Goufo, Cauchy problems with fractal-fractional operators and applications to groundwater dynamics, Fractals, 28 (2020), 1-21
##[5]
A. Atangana, Z. Hammouch, Fractional calculus with power law: The cradle of our ancestors, Eur. Phys. J. Plus, 134 (2019), 1-13
##[6]
Z. Brzeźniak, B. Goldys, Q. T. Le Gia, Random attractors for the stochastic Navier-Stokes equations on the 2D unit sphere, J. Math. Fluid Mech., 20 (2018), 227-253
##[7]
R. M. Ganji, H. Jafari, S. Nemati, A new approach for solving integro-differential equations of variable order, J. Comput. Appl. Math., 379 (2020), 1-13
##[8]
H. Jafari, H. Tajadodi, R. M. Ganji, A numerical approach for solving variable order differential equations based on Bernstein polynomials, Comput. Math. Methods, 1 (2019), 1-11
##[9]
S. Kumar, A. Atangana, A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment, Int. J. Biomath., 13 (2020), 1-17
##[10]
Q. T. Le Gia, Galerkin approximation of elliptic PDEs on spheres, J. Approx. Theory, 130 (2004), 125-149
##[11]
Q. T. Le Gia, Approximation of parabolic PDEs on spheres using collocation method, Adv. Comput. Math., 22 (2005), 377-397
##[12]
Q. T. Le Gia, I. H. Sloan, T. Tran, Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere, Math. Comp., 78 (2009), 79-101
##[13]
Q. T. Le Gia, N. H. Tuan, T. Tran, Solving the backward heat equation on the unit sphere, ANZIAM J. Electron. Suppl., 56 (2014), 262-278
##[14]
N. H. Luc, H. Jafari, P. Kumam, N. H. Tuan, On an initial value problem for time fractional pseudo‐parabolic equation with Caputo derivarive, Mathematical Methods in the Applied Sciences, 2021 (2021), -
##[15]
J. Manimaran, L. Shangerganesh, A. Debbouche, A time-fractional competition ecological model with cross-diffusion, Math. Methods Appl. Sci., 43 (2020), 5197-5211
##[16]
J. Manimaran, L. Shangerganesh, A. Debbouche, Finite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energy, J. Comput. Appl. Math., 382 (2021), 1-11
##[17]
T. B. Ngoc, T. Caraballo, N. H. Tuan, Y. Zhou, Existence and regularity results for terminal value problem for nonlinear super-diffusive fractional wave equations, Nonlinearity, 34 (2021), 1-12
##[18]
T. B. Ngoc, Y. Zhou, D. O'Regan, N. H. Tuan, On a terminal value problem for pseudoparabolic equations involving Riemann-Liouville fractional derivatives, Appl. Math. Lett., 106 (2020), 1-9
##[19]
O. Nikan, H. Jafari, A. Golbabai, Numerical analysis of the fractional evolution model for heat flow in materials with memory, Alexandria Eng. J., 59 (2020), 2627-2637
##[20]
C. V. Pao, Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions, J. Math. Anal. Appl., 195 (1995), 702-718
##[21]
N. D. Phuong, N. H. Luc, Note on a Nonlocal Pseudo-Parabolic Equation on the Unit Sphere, Dyn. Syst. Appl., 30 (2021), 295-304
##[22]
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999)
##[23]
M. Ruzhansky, N. Tokmagambetov, B. T. Torebek, On a non-local problem for a multi-term fractional diffusion-wave equation, Fract. Calc. Appl. Anal., 23 (2020), 324-355
##[24]
K. Sakamoto, M. Yamamoto, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, J. Math. Anal. Appl., 382 (2011), 426-447
##[25]
N. H. Sweilam, S. M. Al-Mekhlafi, T. Assiri, A. Atangana, Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative, Adv. Difference Equ., 2020 (2020), 1-21
##[26]
N. H. Tuan, A. Debbouche, T. B. Ngoc, Existence and regularity of final value problems for time fractional wave equations, Comput. Math. Appl., 78 (2019), 1396-1414
##[27]
N. H. Tuan, L. N. Huynh, T. B. Ngoc, Y. Zhou, On a backward problem for nonlinear fractional diffusion equations, Appl. Math. Lett., 92 (2019), 76-84
##[28]
N. H. Tuan, Y. Zhou, T. N. Thach, N. H. Can, Initial inverse problem for the nonlinear fractional Rayleigh-Stokes equation with random discrete data, Commun. Nonlinear Sci. Numer. Simul., 78 (2019), 1-18
]
Korovkin type approximation theorem via lacunary equi-statistical convergence in fuzzy spaces
Korovkin type approximation theorem via lacunary equi-statistical convergence in fuzzy spaces
en
en
In the present paper, we establish relations between equi-statistical convergence and lacunary equi-statistical convergence of sequences of fuzzy number valued functions. We make an effort to prove Korovkin type approximation theorem via lacunary equi-statistical convergence in fuzzy spaces. Further, we study rates of lacunary equi-statistical fuzzy convergence by using fuzzy modulus of continuity.
312
321
M.
Aiyub
Department of Mathematics, College of Sciences
University of Bahrain
Kingdom of Bahrain
K.
Saini
School of Mathematics
Shri Mata Vaishno Devi University
India
K.
Raj
School of Mathematics
Shri Mata Vaishno Devi University
India
kuldipraj68@gmail.com
Fuzzy number
lacunary equi-statistical convergence
fuzzy rate
fuzzy positive linear operator
Korovkin type approximation theorem
Article.2.pdf
[
[1]
H. Aktuglu, H. Gezer, Lacunary equi-statistical convergence of positive linear operators, Cent. Eur. J. Math., 7 (2009), 558-567
##[2]
G. A. Anastassiou, On basic fuzzy Korovkin theory, Studia Univ. Babes¸-Bolyai Math., 50 (2005), 3-10
##[3]
G. A. Anastassiou, O. Duman, Statistical fuzzy approximation by fuzzy positive linear operators, Comput. Math. Appl., 55 (2008), 573-580
##[4]
S. Aytar, M. A. Mammadov, S. Pehlivan, Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Sets and Systems, 157 (2006), 976-985
##[5]
M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl., 328 (2007), 715-729
##[6]
M. Bas¸arir, M. Mursaleen, Some difference sequences spaces of fuzzy numbers, J. Fuzzy Math., 12 (2004), 1-6
##[7]
C. Belen, S. A. Mohiuddine, Generalized weighted statistical convergence and application, Appl. Math. Comput, 219 (2013), 9821-9826
##[8]
R. Colak, Y. Altin, M. Mursaleen, On some sets of difference sequences of fuzzy numbers, Soft Comput., 15 (2010), 787-793
##[9]
J. Connor, Two valued measure and summability, Analysis, 10 (1990), 373-385
##[10]
O. H. H. Edely, S. A. Mohiuddine, A. K. Noman, Korovkin type approximation theorem obtained through generalized statistical convergence, Appl. Math. Lett., 23 (2010), 1382-1387
##[11]
A. Esi, On Some New Paranormed Sequence Spaces of Fuzzy Numbers Defined By Orlicz Functions and Statistical Convergence, Math. Model. Anal., 11 (2006), 379-388
##[12]
H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244
##[13]
J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313
##[14]
B. Hazarika, A. Alotaibi, S. A. Mohiuddine, Statistical convergence in measure for double sequences of fuzzy-valued functions, Soft Comput.,, 24 (2020), 6613-6622
##[15]
B. Hazarika, A. Esi, On ideal summability and a Korovkin type approximation Theorem, J. Anal., 27 (2019), 1151-1161
##[16]
U. Kadak, S. A. Mohiuddine, Generalized statistically almost convergence based on the difference operator which includes the (p, q)-gamma function and related approximation theorems, Results Math., 73 (2018), 1-31
##[17]
V. Kumar, A. Sharma, K. Kumar, N. Singh, On I-limit points and I-cluster points of sequences of fuzzy numbers, Int. Math. Forum, 2 (2007), 2815-2822
##[18]
H. I. Miller, C. Orhan, On almost convergent and statistically convergent subsequences, Acta Math. Hungar., 93 (2001), 131-151
##[19]
S. A. Mohiuddine, B. A. S. Alamri, Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM,, 113 (2019), 1955-1973
##[20]
S. A. Mohiuddine, A. Asiri, B. Hazarika, Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst., 48 (2019), 492-506
##[21]
S. A. Mohiuddine, B. Hazarika, A. Alotaibi, On statistical convergence of double sequences of fuzzy valued functions, J. Intell. Fuzzy Syst., 32 (2017), 4331-4342
##[22]
M. Mursaleen, A. Alotaibi, Korovkin type approximation theorems for functions of two variables through statistical Asummability, Adv. Difference Equ., 2012 (2012), 1-10
##[23]
M. Mursaleen, M. Basarir, On some new sequences of fuzzy number, Indian J. Pure Appl. Math., 34 (2003), 1351-1357
##[24]
S. Nanda, On sequences of fuzzy number, Fuzzy Sets and Systems, 33 (1989), 123-126
##[25]
F. Nuray, E. Savas, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca, 45 (1995), 269-273
##[26]
S. K. Paikray, P. Parida, S. A. Mohiuddine, A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems, Eur. J. Pure Appl. Math., 13 (2020), 1212-1230
##[27]
M. L. Puri, D. A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl., 91 (1983), 552-558
##[28]
K. Raj, C. Sharma, A. Choudhary, Applications of tauberian theorem in Orlicz spaces of double difference sequences of fuzzy numbers, J. Intell. Fuzzy Syst., 35 (2018), 2513-1524
##[29]
E. Savas, On statistically convergent sequences of fuzzy numbers, Inform. Sci., 137 (2001), 277-282
##[30]
H. Steinhaus, Sur la convergence ordinarie et la convergence asymptotique, Colloq. Math., 2 (1951), 73-74
##[31]
N. Subramanian, A.Esi, Rough statistical convergence on triple sequence of random variables in probability, Trans. A. Razmadze Math. Inst., 173 (2019), 111-120
##[32]
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353
]
On a method for solving nonlinear integro differential equation of order $n$
On a method for solving nonlinear integro differential equation of order $n$
en
en
This work is concerned with the study of a general class of nonlinear integro-differential equations of order n. Using a suitable transformation, we derive an equivalent nonlinear Fredholm-Volterra integral equation (NF-VIE) to this class of equations. The existence of continuous solutions for the NF-VIE is investigated subject to the verification of some sufficient conditions. We apply the modified Adomian's decomposition method (MADM) and homotopy analysis method (HAM) to solve this NF-VIE. The convergence and error estimate of the approximate solution are also studied. The numerical results in this article show that the HAM technique may give an approximate solution with high accuracy and convergence rate faster than the one obtained using the MADM technique provided the convergence control parameter \(\hbar\) is properly chosen when applying the HAM.
322
340
M. A.
Abdou
Department of Mathematics, Faculty of Education
Alexandria University
Egypt
abdella_777@yahoo.com
M. I.
Youssef
Department of Mathematics, College of Science
Department of Mathematics, Faculty of Education
Jouf University
Alexandria University
Saudi Arabia
Egypt
miyoussef283@gmail.com
Integro-differential equations
existence
uniqueness
modified Adomian's decomposition method
homotopy analysis method
Article.3.pdf
[
[1]
G. Adomian, Stochastic Systems, Academic Press, Orlando (1983)
##[2]
G. Adomian, Nonlinear Stochastic Operator Equations, Academic Press, Orlando (1986)
##[3]
G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers Group, Dordrecht (1994)
##[4]
R. P. Agarwal, M. Meehan, D. O'Regan, Fixed Point Theory and Applications, Cambridge University Press, Cambridge (2001)
##[5]
A. Alidema, A. Georgieva, Adomian decomposition method for solving two-dimensional nonlinear Volterra Fuzzy integral equations, AIP Conference Proceedings, 2018 (2018), 1-11
##[6]
H. O. Bakodah, M. Al-Mazmumy, S. O. Almuhalbedi, Solving system of integro differential equations using discrete Adomian decomposition method, J. Taibah Univ. Sci., 13 (2019), 805-812
##[7]
M. M. Elborai, M. A. Abdou, M. I. Youssef, On Adomian's decomposition method for solving nonlocal perturbed stochastic fractional integro-differential equations, Life Sci. J., 10 (2013), 550-555
##[8]
I. L. El-Kalla, Error analysis of Adomian series solution to a class of nonlinear differential equations, Appl. Math. E-Notes, 7 (2007), 214-221
##[9]
A. Hamoud, A. Azeez, K. Ghadle, A study of some iterative methods for solving Fuzzy Volterra-Fredholm integral equations, Indones. J. Ele. Eng. Comput. Sci., 11 (2018), 1228-1235
##[10]
A. A. Hamoud, K. P. Ghadle, The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques, Probl. Anal. Issues Anal., 7 (2018), 41-58
##[11]
A. Hamoud, K. Ghadle, Modified Adomian decomposition method for solving Fuzzy Volterra-Fredholm integral equations, J. Indian Math. Soc., 85 (2018), 53-69
##[12]
A. A. Hamoud, K. P. Ghadle, Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations, J. Math. Model., 6 (2018), 91-104
##[13]
A. A. Hamoud, K. P. Ghadle, Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind, Tamkang J. Math., 49 (2018), 301-315
##[14]
A. A. Hamoud, K. P. Ghadle, S. M. Atshan, The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method, Khayyam J. Math., 5 (2019), 21-39
##[15]
J. H. He, A short review on analytical methods for to a fully fourth-order nonlinear integral boundary value problem with fractal derivatives, Inter. J. Numer. Methods Heat Fluid Flow, 39 (2020), 4933-4943
##[16]
E. Hetmaniok, D. Slota, T. Trawinski, R. Witula, Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind, Numer. Algorithms, 67 (2014), 163-185
##[17]
M. H. Holmes, Introduction to Perturbation Methods, Springer, New York (2013)
##[18]
M. Issa, A. Hamoud, K. Ghadle, Numerical solutions of Fuzzy integro-differential equations of the second kind, J. Math. Computer Sci., 23 (2021), 67-74
##[19]
A. Kurt, O. Tasbozan, Approximate analytical solutions to conformable modified Burgers equation using homotopy analysis method}, Ann. Math. Sil., 33 (2019), 159-167
##[20]
S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University (1992)
##[21]
S. J. Liao, Beyond Perturbation Introduction to the Homotopy Analysis Method, Chapman and Hall/CRC, U.S.A. (2003)
##[22]
S. J. Liao, Homotopy Analysis Method in Nonlinear Differential Equation, Springer, New York (2012)
##[23]
S. J. Liao, Advances In The Homotopy Analysis Method, World Scientific Publishing Co., Hackensack (2014)
##[24]
S. Maitama, W. D. Zhao, Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets, Adv. Difference Equ., 2019 (2019), 1-22
##[25]
M. Marino, Instantons and large N: An Introduction to Non-Perturbative Methods in Quantum Field Theory, Cambridge University Press, Cambridge (2015)
##[26]
T. Muta, Foundations of Quantum Chromodynamics: An Introduction to Perturbative Methods in Gauge Theories, Third ed., World Scientific Pub. Co., Hackensack (2010)
##[27]
A. H. Nayfeh, Perturbation Methods, Wiley-Interscience, New York (2000)
##[28]
J. Singh, D. Kumar, D. Baleanu, S. Rathore, An efficient numerical algorithm for the fractional drinfeld-sokolov-wilson equation, Appl. Math. Comput., 335 (2018), 12-24
##[29]
R. Singh, G. Nelakanti, J. Kumar, Approximate solution of Urysohn integral equations using the Adomian decomposition method, Sci. World J., 2014 (2014), 1-6
##[30]
A. M. Wazwaz, A reliable modification of Adomian decomposition method, Appl. Math. Comput., 102 (1999), 77-86
##[31]
L.-J. Xie, A new modification of Adomian decomposition method for Volterra integral equations of the second kind, J. Appl. Math., 2013 (2013), 1-7
]
Prevalent fixed point theorems on MIFM-Spaces using the (\(CLR_{SR}\)) property and implicit function
Prevalent fixed point theorems on MIFM-Spaces using the (\(CLR_{SR}\)) property and implicit function
en
en
The main goal of this study is to use an implicit function to demonstrate the existence of a common fixed point on modified intuitionistic fuzzy metric spaces by using the concept of common limit range property with regard to two self-mappings \(S\) and \(R\), i.e., (\(CLR_{SR}\)) property. Our primary result is supported by an example that validates the hypotheses of our result. Our findings improve and generalize the findings of Tanveer et al. [M. Tanveer, M. Imdad, D. Gopal, D. K. Patel, Fixed Point Theory Appl., \(\bf 2012\) (2012), 1--12], and other existing results related to this study.
341
350
P. K.
Sharma
Department of Mathematics
SVIS, Shri Vaishnav Vidyapeeth Vishwavidyalaya
India
praveen_jan1980@rediffmail.com
Sh.
Sharma
Department of Mathematics
Govt. P. G. College
India
Common fixed point
common property (E-A)
common limit in range property (CLR property)
implicit function
Article.4.pdf
[
[1]
M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188
##[2]
H. M. Abu-Donia, A. A. Nasef, Common fixed point theorems in intuitionistic fuzzy metric spaces, Fuzzy Syst. Math., 22 (2008), 100-106
##[3]
C. Alaca, D. Turkoglu, C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 29 (2006), 1073-1078
##[4]
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96
##[5]
G. V. R. Babu, P. Subhashini, Coupled common fixed point theorems of Cir´ic type g-weak contractions with CLRg property, Journal of Nonlinear Analysis and Optimization, 4 (2013), 133-145
##[6]
L. B. Ciric, S. N. Jesic, J. S. Ume, The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 37 (2008), 781-791
##[7]
S. Chauhan, M. Imdad, B. Samet, Coincidence and common fixed point theorems in modified intuitionistic fuzzy metric spaces, Math. Comput. Model., 58 (2013), 898-906
##[8]
S. Chauhan, M. Imdad, C. Vetro, Unified metrical common fixed point theorems in 2-metric spaces via an implicit relation, Journal of Operators, 2013 (2013), 1-11
##[9]
S. Chauhan, M. A. Khan, S. Kumar, Unified fixed point theorems in fuzzy metric spaces via common limit range property, J. Inequal. Appl., 2013 (2013), 1-17
##[10]
S. Chauhan, M. A. Khan, W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces satisfying φ-contractive condition with common limit range property, Abstract and Applied Analysis, 2013 (2013), 1-14
##[11]
S. Chauhan, B. D. Pant, S. Radenovic, Common fixed point theorems for R-weakly commuting mappings with a common limit in the range property, J. Indian Math. Soc., 81 (2014), 13-14
##[12]
D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), 81-89
##[13]
G. Deschrijver, C. Cornelis, E. E. Kerre, On the representation of intuitionistic fuzzy t-norm and t-conorm, IEEE Transactions on Fuzzy Systems, 12 (2004), 45-61
##[14]
G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, 133 (2003), 227-235
##[15]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399
##[16]
V. Gregori, S. Romaguera, P. Veeramani, A note on intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 28 (2006), 902-905
##[17]
U. Gul, E. Karapınar, On almost contractions in partially ordered metric spaces via implicit relations, J. Inequal. Appl., 2012 (2012), 1-11
##[18]
S. Gulyaz, E. Karapınar, I S. Yuce, A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation, Fixed Point Theory Appl., 2013 (2013), 1-11
##[19]
V. Gupta, R. K. Saini, A. Kanwar, Some coupled fixed point results on modified intuitionistic fuzzy metric spaces and application to integral type contraction, Iran. J. Fuzzy Syst., 14 (2017), 123-137
##[20]
X. Huang, C. Zhu, X. Wen, Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56 (2010), 305-326
##[21]
N. M. Hung, E. Karapınar, N. V. Luong, Coupled coincidence point theorem in partially ordered metric spaces via implicit relation, Abstr. Appl. Anal., 2012 (2012), 1-14
##[22]
M. Imdad, J. Ali, M. Hasan, Common fixed point theorems in modified intuitionistic fuzzy metric spaces, Iran. J. Fuzzy Syst., 9 (2012), 77-92
##[23]
M. Imdad, J. Ali, M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos Solitons Fractals, (), -
##[24]
M. Imdad, S. Chauhan, Employing common limit range property to prove unified metrical common fixed point theorems, Int. J. Anal.,, 2013 (2013), 1-10
##[25]
M. Imdad, B. D. Pant, S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST) property and applications, J. Nonlinear Anal. Optim., 3 (2012), 225-237
##[26]
S. Jain, S. Jain, L. Bahadur Jain, Compatibility of type (P) in modified intuitionistic fuzzy metric space, J. Nonlinear Sci. Appl., 3 (2010), 96-109
##[27]
M. Jain, K. Tas, S. Kumar, N. Gupta, Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg property in fuzzy metric spaces, J. Appl. Math., 2012 (2012), 1-13
##[28]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), -
##[29]
G. Jungck, B. E. Rhoades, Fixed points for set-valued functions without continuity, Indian J. Pure Appl. Math., 29 (1998), 227-238
##[30]
M. Kumar, P. Kumar, S. Kumar, Some common fixed point theorems using (CLRg) property in cone metric spaces, Adv. Fixed Point Theory, 2 (2012), 340-356
##[31]
Y. Liu, J. Wu, Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci., 19 (2005), 3045-3055
##[32]
T. K. Mondal, S. K. Samanta, On intuitionistic gradation of openness, Fuzzy Sets and Systems, 131 (2002), 323-336
##[33]
R. P. Pant, Common fixed point theorems for contractive maps, J. Math. Anal. Appl., 226 (1998), 251-258
##[34]
B. D. Pant, S. Kumar, S. Chauhan, Common fixed point of weakly compatible maps on intuitionistic fuzzy metric spaces, J. Adv. Stud. Topol., 1 (2010), 41-49
##[35]
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 22 (2004), 1039-1046
##[36]
R. Saadati, S. Sedghi, N. Shobe, Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos Solitons Fractals, 38 (2008), 36-47
##[37]
S. Sedghi, N. Shobe, A. Aliouche, Common fixed point theorems in intuitionistic fuzzy metric spaces through conditions of integral type, Appl. Math. Inf. Sci., 2 (2008), 61-82
##[38]
P. K. Sharma, Some common fixed point theorems for a sequence of self mappings in fuzzy metric space with property (CLRg), J. Math. Comput. Sci., 10 (2020), 1499-1509
##[39]
S. Sharma, B. Deshpande, Common fixed point theorems for a finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 40 (2009), 2242-2256
##[40]
W. Shatanawi, V. Gupta, A. Kanwar, New results on modified intuitionistic generalized fuzzy metric spaces by employing E.A property and common E.A property for coupled maps, Journal of Intelligent and Fuzzy Systems, 38 (2020), 3003-3010
##[41]
W. Sintunavarat, S. Chauhan, P. Kumam, Some fixed point results in modified intuitionistic fuzzy metric spaces, Afr. Mat., 25 (2014), 461-473
##[42]
W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), 1-14
##[43]
W. Sintunavarat, P. Kumam, Fixed point theorems for a generalized intuitionistic fuzzy contraction in intuitionistic fuzzy metric spaces, Thai J. Math., 10 (2012), 123-135
##[44]
W. Sintunavarat, P. Kumam, Common fixed points for R-weakly commuting in fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat., 58 (2012), 389-406
##[45]
M. Tanveer, M. Imdad, D. Gopal, D. K. Patel, Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A.), Fixed Point Theory Appl., 2012 (2012), 1-12
##[46]
R. K. Verma, H. K. Pathak, Common fixed point theorems using property (E.A) in complex-valued metric spaces, Thai J. Math., 11 (2013), 347-355
##[47]
L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353
]
Oscillation conditions of the second-order noncanonical difference equations
Oscillation conditions of the second-order noncanonical difference equations
en
en
We derive new oscillatory conditions for the second-order noncanonical difference equations of the type
\[
\Delta ( r(\nu) \Delta x(\nu) ) + q(\nu) x (\nu+\sigma) = 0, \quad \nu\geq \nu_0,\]
by creating monotonical properties of nonoscillatory solutions. Our oscillatory outcomes are effectively an extension of the previous ones. We provide several examples to demonstrate the efficacy of the new criteria.
351
360
P.
Gopalakrishnan
Department of Mathematics
Mahendra Arts \(\&\) Science College (Autonomous)
India
A.
Murugesan
Department of Mathematics
Government Arts College (Autonomous)
India
amurugesan3@gmail.com
C.
Jayakumar
Department of Mathematics
Mahendra Arts \(\&\) Science College (Autonomous)
India
Oscillation
nonoscillation
second-order
canonical
noncanonical
delay
difference equations
Article.5.pdf
[
[1]
R. P. Agarwal, S. R. Grace, D. O'Regan, On the oscillation of certain third-order difference equations, Adv. Difference Equ., 2005 (2005), 345-367
##[2]
R. P. Agarwal, S. R. Grace, D. O'Regan, Oscillation Theory for Difference and Functional Difference Equations, Springer Science & Business Media, Berlin/Heidelberg (2013)
##[3]
R. P. Agarwal, M. M. S. Manuel, E. Thandapani, Oscillatory and nonoscillatory behavior of second order neutral delay difference equations, Math. Comput. Modelling, 24 (1996), 5-11
##[4]
R. P. Agarwal, P. J. Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers Group, Dodrecht (1997)
##[5]
R. Arul, E. Thandapani, Asymptotic behavior of positive solutions of second order quasilinear difference equations, Kyungpook Math. J., 40 (2000), 275-286
##[6]
B. Baculikova, Oscillatory behavior of the second order noncanonical differential equations, Electron. J. Qual. Theory Differ. Equ., 89 (2019), 1-11
##[7]
J. Banasiak, Modelling with Difference and Differential Equations, Cambridge University Press, Cambridge (1997)
##[8]
S. R. Grace, J. Alzabut, Oscillation results for nonlinear second order difference equations with mixed neutral terms, Adv. Difference Equ., 2020 (2020), 1-12
##[9]
I. Györi, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford (1991)
##[10]
D. L. Jagerman, Difference Equations with Applications to Queues, Marcel Dekker, Inc., New York (2000)
##[11]
W.-T. Li, Oscillation Theorem for second order nonlinear difference equations, Math. Comput. Modelling, 31 (2000), 71-79
##[12]
W.-T. Li, S. S. Cheng, Classifications and existence of positive solutions of second order nonlinear neutral difference equations, Funkcial. Ekvac., 40 (1997), 371-393
##[13]
H.-J. Li, C.-C. Yeh, Oscillation criteria for second order neutral delay difference equations, Comput. Math. Appl., 36 (1998), 123-132
##[14]
R. E. Mickens, Difference Equations, Third edition, CRC Press, Boca Raton (2015)
##[15]
A. Murugesan, Oscillation of neutral advanced difference equation, Global J. Pure Appl. Math., 9 (2013), 83-92
##[16]
A. Murugesan, K. Ammamuthu, Sufficient conditions for oscillation of second order neutral advanced difference equations, Int. J. Pure Appl. Math., 98 (2015), 145-156
##[17]
A. Murugesan, C. Jayakumar, Oscillation condition for second order half-linear advanced difference equation with variable coefficients, Malaya J. Mat., 8 (2020), 1872-1879
##[18]
B. Ping, M. Han, Oscillation of second order difference equations with advanced argument, Discrete Contin. Dyn. Syst., 2003 (2003), 108-112
##[19]
S. H. Saker, Oscillation of second order nonlinear delay difference equations, Bull. Korean Math. Soc., 40 (2003), 489-501
##[20]
E. Thandapani, I. Győri, B. S. Lalli, An application of discrete inequality to second order nonlinear oscillation, J. Math. Anal. Appl., 186 (1994), 200-208
##[21]
B. G. Zhang, G. D. Chen, Oscillation of certain second order nonlinear difference equation, J. Math. Anal. Appl., 199 (1996), 827-841
]
Joint \(n\)-normality of linear transformations
Joint \(n\)-normality of linear transformations
en
en
This paper is concerned with studying a new class of multivariable operators know as joint \(n\)-normal \(q\)-tuple of operators.
Some structural properties of some members of this class are given.
361
369
A. A.
AL-Dohiman
Mathematical Analysis and Applications, Mathematics Department, College of Science
Jouf University
Saudi Arabia
a.aldohiman@ju.edu.sa
\(n\)-normal
joint \(n\)-normal
tensor product
Article.6.pdf
[
[1]
E. H. Abood, M. A. Al-loz, On some generalizations of $(n,m)$-normal powers operators on Hilbert space, J. Progress. Res. Math., 7 (1978), 113-114
##[2]
E. H. Abood, M. A. Al-loz, On some generalization of normal operators on Hilbert space, Iraqi J. Sci., 56 (2015), 1786-1794
##[3]
S. A. O. Ahmed Mahmoud, On the joint class of $(m, q)$-partial isometries and the joint $m$-invertible tuples of commuting operators on a Hilbert space, Ital. J. Pure Appl. Math., 40 (2018), 438-463
##[4]
S. A. O. Ahmed Mahmoud, M. Chō, J. E. Lee, On $(m,C)$-Isometric Commuting Tuples of Operators on a Hilbert Space, Results Math., 73 (2018), 1-31
##[5]
S. A. O. Ahmed Mahmoud, O. B. Sid Ahmed, On the classes of $(n, m)$-power $D$-normal and $(n,m)$-power $D$-quasi-normal operators, Oper. Matrices, 13 (2019), 705-732
##[6]
S. A. Alzuraiqi, A. B. Patel, On $n$-Normal Operators, General Math. Notes, 1 (2020), 61-73
##[7]
M. Chō, S. A. O. Ahmed Mahmoud, $(A,m)$-Symmetric commuting tuple of operators on a Hilbert space, J. Inequalities Appl., 22 (2019), 1-12
##[8]
M. Chō, E. M. O. Beiba, S. A. O. Ahmed Mahmoud, $(n_1,\cdots, n_p)$-quasi-$m$-isometric commuting tuple of operators on a Hilbert space, Ann. Funct. Anal., 12 (2021), 1-18
##[9]
M. Chō, J. E. Lee, K. Tanahashic, A. Uchiyamad, Remarks on $n$-normal Operators, Filomat, 32 (2018), 5441-5451
##[10]
M. Chō, B. N. Načevska, Spectral properties of $n$-normal operators, Filomat, 3 (2018), 5063-5069
##[11]
R. E. Curto, S. H. Lee, J. Yoon, $k$-Hyponormality of multivariable weighted shifts, J. Funct. Anal., 229 (2005), 462-480
##[12]
R. E. Curto, S. H. Lee, J. Yoon, Hyponormality and subnormality for powers of commuting pairs of subnormal operators, J. Funct. Anal., 245 (2007), 390-412
##[13]
D. S. Djordjević, M. Chō, D. Mosić, Polynomially normal operators, J. Funct. Anal., 11 (2020), 493-504
##[14]
J. Gleason, S. Richter, $m$-Isometric Commuting Tuples of Operators on a Hilbert Space, Integral Equations Operator Theory, 56 (2006), 181-196
##[15]
M. Guesba, E. M. O. Beiba, S. A. O. Ahmed Mahmoud, Joint $A$-hyponormality of operators in semi-Hilbert spaces, Linear and Multilinear Algebra, 67 (2019), 1-20
##[16]
P. H. W. Hoffmann, M. Mackey, $(m, p)$-isometric and $(m, \infty)$-isometric operator tuples on normed spaces, Asian-Eur. J. Math., 8 (2015), 1-32
##[17]
A. A. S. Jibril, On $n$-Power Normal Operators, Arab. J. Sci. Eng. Sect. A Sci., 33 (2008), 247-251
##[18]
I. Kaplansky, Products of normal operators, Duke Math. J., 20 (1953), 257-260
##[19]
J. Stochel, Seminormality of operators from their tensor product, Proc. Amer. Math. Soc., 124 (1996), 135-140
]
On admissible curves and their evolution equations in pseudo-Galilean space
On admissible curves and their evolution equations in pseudo-Galilean space
en
en
The evolution equations of some forms of admissible curves in the pseudo-Galilean Space \(G_{3}^1\) are investigated in this paper. In more detail, we use two separate methods to obtain coupled nonlinear partial differential equations of time evolution in terms of their curvatures. The first method studies the evolution equations for admissible curves via the frame field, while the second studies the evolution equations via the velocity vector. Then, the position vectors of the evolving curves are formulated. Also, we conduct comparative research of the evolution equations for curves in different spaces. We furthermore present some models as an application of the evolution equations of the curvature and torsion for admissible curves, confirming our theoretical results.
370
380
H. S.
Abdel-Aziz
Department of Mathematics
Sohag University
Egypt
habdelaziz2005@yahoo.com
H. M.
Serry
Department of Mathematics
Suez Canal University
Egypt
hebamserry@gmail.com
F. M.
El-Adawy
Department of Mathematics
Suez Canal University
Egypt
fmorsi88@yahoo.com
A. A.
Khalil
Department of Mathematics
Sohag University
Egypt
amalaboelwafa@yahoo.com
Admissible curves
evolution equations
Frenet frame
pseudo-Galilean space
spacelike and timelike curves
Article.7.pdf
[
[1]
N. H. Abdel-All, M. A. Abdel-Razek, H. S. Abdel-Aziz, A. A.Khalil, Geometry of evolving plane curves problem via lie group analysis, Stud. Math. Sci., 2 (2011), 51-62
##[2]
N. H. Abdel-All, R. A. Hussien, T. Youssef, Evolution of curves via the velocities of the moving frame, J. Math. Comput. Sci., 2 (2012), 1170-1185
##[3]
N. H. Abdel-All, S. G. Mohamed, M. T. Al-Dossary, Evolution of generalized space curve as a function of its local geometry, Appl. Math., 5 (2014), 2381-2392
##[4]
K. Alkan, S. C. Anco, Integrable systems from inelastic curve flows in 2and 3dimensional Minkowski space, J. Nonlinear Math. Phys., 23 (2016), 256-299
##[5]
R. Balakrishnan, R. Blumenfeld, Transformation of general curve evolution to a modified Belavin-Polyakov equation, J. Math. Phys., 38 (1997), 5878-5888
##[6]
D. Baldwin, Ü.Göktaş, W. Hereman, L. Hong, R. S. Martino, J. C. Miller, Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs, J. Symbolic Comput., 37 (2004), 669-705
##[7]
S. Cengiz, E. B. Koc Ozturk, U. Ozturk, Motions of curves in the pseudo-Galilean space $G^1_3$, Math. Probl. Eng., 2015 (2015), 1-6
##[8]
M. Dede, C. Ekici, On parallel ruled surfaces in Galilean space, Kragujevac J. Math.,, 40 (2016), 47-59
##[9]
M. Desbrun, M.-P. Cani, Active implicit surface for animation, In: Proc. Graphics Interface--Canadian Inf. Process. Soc., 1998 (1998), 143-450
##[10]
Q. Ding, W. Wang, Y. Wang, A motion of spacelike curves in the Minkowski 3-space and the KdV equation, Phys. Lett. A, 374 (2010), 3201-3205
##[11]
B. Divjak, Geometrija pseudogalilejevih prostora, Ph.D. Thesis, University of Zagreb, Zagreb (1997)
##[12]
B. Divjak, Curves in pseudo-Galilean geometry, Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 41 (1998), 119-130
##[13]
B. Divjak, Z. Milin-Šipuš, Special curves on ruled surfaces in Galilean and pseudo-Galilean spaces, Acta Math. Hungar.,, 98 (2003), 203-215
##[14]
B. Divjak, Z. Milin-Šipuš, Minding isometries of ruled surfaces in pseudo-Galilean space, J. Geom., 77 (2003), 35-47
##[15]
C. Ekici, M. Dede, On the Darboux vector of ruled surfaces in pseudo-Galilean space, Math. Comput. Appl., 16 (2011), 830-838
##[16]
A. S. Fokas, J. Lenells, A new approach to integrable evolution equations on the circle, Proc. A., 477 (2021), 1-28
##[17]
M. Gage, R. S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geom., 23 (1986), 69-96
##[18]
E. F. D. Goufo, I. T. Toudjeu, Analysis of recent fractional evolution equations and applications, Chaos Solitons Fractals, 126 (2019), 337-350
##[19]
M. A. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom., 26 (1987), 285-314
##[20]
N. Gürbüz, Three classes of non-lightlike curve evolution according to Darboux frame and geometric phase, Int. J. Geom. Methods Mod. Phys., 15 (2018), 1-16
##[21]
H. Hasimoto, A soliton on a vortex filament, J. Fluid Mech., 51 (1972), 477-485
##[22]
M. Hisakado, M. Wadati, Moving discrete curve and geometric phase, Phys. Lett. A, 214 (1996), 252-258
##[23]
Z. Kucukarslan-Yuzbasi, E. Cavlak-Aslan, M. Inc, D. Baleanu, On exact solutions for new coupled nonlinear models getting evolution of curves in Galilean space, Therm. Sci., 23 (2019), 227-233
##[24]
G. L. Lamb Jr, Solitons on moving space curves, J. Mathematical Phys., 18 (1977), 1654-1661
##[25]
H. Q. Lu, J.S. Todhunter, T. W. Sze, Congruence conditions for nonplanar developable surfaces and their application to surface recognition, CVGIP: Image Understanding, 58 (1993), 265-285
##[26]
K. Nakayama, Motion of curves in hyperboloid in the Minkowski space, J. Phys. Soc. Japan, 67 (1998), 3031-3037
##[27]
K. Nakayama, H. Segur, M. Wadati, Integrability and the motion of curves, Phys. Rev. Lett., 69 (1992), 2603-2606
##[28]
H. Oztekin, H. G. Bozok, POSITION VECTORS OF ADMISSIBLE CURVES IN 3-DIMENSIONAL PSEUDOGALILEAN SPACE $G^1_3$, Int. Electron. J. Geom., 8 (2015), 21-32
##[29]
A. I. Prilepko, A. B. Kostin, I. V. Tikhonov, Inverse problems for evolution equations, De Gruyter, 2020 (2020), 379-389
##[30]
A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press, Boca Raton (1998)
##[31]
J. A. Sethian, Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, Cambridge university press, Cambridge (1999)
##[32]
D. J. Unger, Developable surfaces in elastoplastic fracture mechanics, Int. J. Fract., 50 (1991), 33-38
##[33]
I. Waini, A. Ishak, I. Pop, Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid, Int. J. Heat Mass Transf., 136 (2019), 288-397
##[34]
F. Yang, Sun, Y.-R. Li, H. X.-X. Li, C.-Y. Huang, The quasi-boundary value method for identifying the initial value of heat equation on a columnar symmetric domain, Numer. Algorithms, 82 (2019), 623-639
##[35]
O. G. Yıldız, M. Tosun, A note on evolution of curves in the Minkowski spaces, Adv. Appl. Clifford Algebr., 27 (2017), 2873-2884
]
On periodicity of systems of rational difference equations
On periodicity of systems of rational difference equations
en
en
In this paper, we investigate the periodicity of two systems of rational sequences of second and third order, respectively. The systems include a permutation that gives the ability of changing the appearance of components of solutions in the equations of the systems.
We find periods of systems in terms of the order of the permutation.
The periodicity of two more systems of maximum type are studied.
Finally, many illustrative examples are given.
381
390
A. E.
Hamza
Department of Mathematics, College of Science
University of Jeddah
Saudi Arabia
hamzaaeg2003@yahoo.com
N.
Alsulami
Department of Mathematics, Faculty of Science
Cairo University
Egypt
nasir6655@hotmail.com
Systems of difference equations
permutation groups
periodicity
Article.8.pdf
[
[1]
O. Bogopolski, Introduction to group theory, Cambridge University Press, Cambridge (1994)
##[2]
F. A. Cotton, Chemical applications of group theory, John Wiley & Sons, New York (1990)
##[3]
S. Elaydi, An introduction to difference equations, Third Edition, Springer, New York (2005)
##[4]
E. M. Elsayed, A. Alotaibi, H. A. Almaylabi, On the periodicity and solutions of some difference equations systems, J. Comput. Theor. Nanosci., 13 (2016), 1624-1628
##[5]
E. M. Elsayed, T. F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations, Hacet. J. Math. Stat., 44 (2015), 1361-1390
##[6]
E. M. Elsayed, F. Alzahrani, I. Abbas, N. H. Alotaibi, Solutions of some difference equations systems and periodicity, J. Adv. Math., 16 (2019), 8247-8261
##[7]
E. M. Elsayed, H. El-Metwally, On the solutions of some nonlinear systems of difference equations, Adv. Difference Equ., 2013 (2013), 1-14
##[8]
T. W. Hungerford, Algebra, Springer-Verlag, New York (1974)
##[9]
B. D. Iričanin, S. Stević, Some systems of nonlinear difference equations of higher order with periodic solutions, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 13 (2006), 499-507
##[10]
M. R. S. Kulenovic, G. Ladas, Dynamics of second order rational difference equations, with open problems and conjectures, Chapman and Hall/CRC, New York (2001)
##[11]
R. C. Lyness, Notes 1581, Math. Gaz, 26 (1942), 62-63
##[12]
R. C. Lyness, Notes 1847, Math. Gaz, 29 (1945), 231-233
##[13]
R.C. Lyness, Notes 2952, Math. Gaz, 45 (1961), 207-209
##[14]
H. Bao, Dynamical behavior of a system of second-order nonlinear difference equations, Int. J. Differ. Equ., 2015 (2015), 1-7
##[15]
C. J. Schinas, Invariants for difference equations and systems of difference equations of rational form, J. Math. Anal. Appl., 216 (1997), 164-179
##[16]
S. Sternberg, Group theory and physics, Cambridge University Press, Cambridge (1994)
##[17]
S.Stevic, M. A. Alghamdi, D. A. Maturi, N. Shahzad, On the periodicity of some classes of systems of nonlinear difference equations, Abstr. Appl. Anal., 2014 (2014), 1-6
]