]>
2020
13
4
ISSN 2008-1898
0
On the solution of Wave-Schrodinger equation
On the solution of Wave-Schrodinger equation
en
en
In this paper, we are finding a solution of the fractional Wave-Schrodinger equation by Laplace transform in the sense of Caputo fractional derivative. It was found that
the fundamental solution of the equation is related to Wright function.
176
179
Wanchak
Satsanit
Department of Mathematics, Faculty of Science
Maejo University
Thailand
wanchack@gmail.com
Dirac delta distribution
Laplacian operator
Wright function
Article.1.pdf
[
[1]
A. Kananthai, On the Solution of the n-Dimensional Diamond Operator, Appl. Math. Comput., 88 (1997), 27-37
##[2]
A. Kananthai, S. Suantai, V, Longani, On the operator $\oplus^{k}$ related to the wave equation and Laplacian, Appl. Math. Comput., 132 (2002), 219-229
##[3]
I. Podlubny, Fractional Differential Equations, Acedemic Press, San Diego (1999)
##[4]
L. G. Romero, A generalization of the Laplacian operator, Palest. J. Math., 5 (2016), 204-207
]
Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach
Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach
en
en
In this article, we establish the existence of solutions for a functional integral equation of fractional order.
The study upholds the case when the set-valued function has \(L^1\)-Caratheodory selections, we reformulate the functional integral inclusion according to these selections via a classical fixed point theorem of Schauder and present theorem for the existence of integrable solutions.
As an application, the existence of solutions of nonlinear functional integro-differential inclusion with an initial value,
and the initial value problem for the arbitrary-order differential inclusion will be studied.
180
186
A. M. A.
El-Sayed
Faculty of Science
Alexandria University
Egypt
amasayed@alexu.edu.eg
Sh. M.
Al-Issa
Faculty of Science
Faculty of Science
Lebanes International University
The International University of Beirut
Lebanon
Lebanon
shorouk.alissa@liu.edu.lb
Fractional calculus
integro-differential inclusion
\(L^1\)-Caratheodory selections
Schauder fixed point principle
Kolmogorov compactness criterion
Article.2.pdf
[
[1]
S. Al-Issa, A. M. A. El-Sayed, Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders, Comment. Math., 49 (2009), 171-177
##[2]
J.-P. Aubin A. Cellina, Differential Inclusion, Springer-Verlag, Berlin (1984)
##[3]
J. Banaś, On the superposition operator and integrable solutions of some functional equations, Nonlinear Anal., 12 (1988), 777-784
##[4]
J. Banaś, Integrable solutions of Hammerstein and Urysohn integral equations, J. Austral. Math. Soc. Ser. A, 46 (1989), 61-68
##[5]
F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl., 20 (1967), 197-228
##[6]
A. Cellina, S. Solimini, Continuous extensions of selections, Bull. Polish Acad. Sci. Math., 35 (1989), 573-581
##[7]
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin (1985)
##[8]
B. C. Dhage, A functional integral inclusion involving discontinuities, Fixed Point Theory, 5 (2004), 53-64
##[9]
J. Dugundji,, A. Granas, Fixed Point Theory, Państwowe Wydawnictwo Naukowe (PWN), Warsaw (1982)
##[10]
A. M. A. El-Sayed, A.-G. Ibrahim, Multivalued fractional differential equations, Appl. Math. Comput., 68 (1995), 15-25
##[11]
A. M. A. El-Sayed, A.-G. Ibrahim, Set-valued integral equations of fractional-orders, Appl. Math. Comput., 118 (2001), 113-121
##[12]
A. M. A. El-Sayed, S. M. Al-Issa, Monotonic continuous solution for a mixed type integral inclusion of fractional order, J. Math. Appl., 33 (2010), 27-34
##[13]
A. M. A. El-Sayed, S. M. Al-Issa, Existence of continuous solutions for nonlinear functional differential and integral inclusions, Malaya J. Mat., 7 (2019), 541-544
##[14]
A. M. A. El-Sayed, S. M. Al-Issa, Monotonic integrable solution for a mixed type integral and differential inclusion of fractional orders, Int. J. Differ. Equations Appl., 18 (2019), 1-10
##[15]
A. M. A. El-Sayed, S. M. Al-Issa, Monotonic solutions for a quadratic integral equation of fractional order, AIMS Mathematics, 4 (2019), 821-830
##[16]
G. Emmanuele, Integrable solutions of Hammerstein integral equations, Appl. Anal., 50 (1993), 277-284
##[17]
A. Fyszkowski, Continuous selection for a class of non-convex multivalued maps, Studia Math., 76 (1983), 163-174
##[18]
A.-G. Ibrahim, A. M. A. El-Sayed, Definite integral of fractional order for set-valued function, J. Fract. Calc., 11 (1997), 81-87
##[19]
K. Kuratowski, C. Ryll-Nardzewski, Ageneral theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 13 (1965), 397-403
##[20]
K. S. Miller, B. Ross, An Introduction to the fractional calculus and fractional differential equations, John Wiley & Sons, New York (1993)
##[21]
D. O'Regan, Integral inclusions of upper semi-continuous or lower semi-continuous type, Proc. Amer. Math. Soc., 124 (1996), 2391-2399
##[22]
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999)
##[23]
I. Podlubny, A. M. A. EL-Sayed, On two defintions of fractional calculus, Solvak Academy Sci.-Ins. Eyperimental Phys., 1996 (1996), 3-96
##[24]
S. G. Samko, A. A. Kilbas, O. I. Marichev, Integrals and Derivatives of Fractional Orders and Some of their Applications, Nauka i Teknika, Minsk (1987)
##[25]
C. Swartz, Measure, integration and function spaces, World Scientific Publishing Co., River Edge (1994)
]
Stability, controllability, and observability criteria for state-space dynamical systems on measure chains with an application to fixed point arithmetic
Stability, controllability, and observability criteria for state-space dynamical systems on measure chains with an application to fixed point arithmetic
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en
In this paper, our main attempt is to unify results on stability, controllability, and observability criteria on real-time dynamical systems with non-uniform domains. The results of continuous/discrete systems will now become a particular case of our results. As an application a first-order time scale dynamical system on measure chains in one-dimensional state space having both continuous/discrete filters to minimize the effect of a round of noise at the filter outputs is presented. A set of necessary and sufficient conditions for this dynamical system to be stable and completely stable are established.
187
195
Yan
Wu
Department of Mathematical Sciences
Georgia Southern University
USA
Sailaja
P
Department of Mathematics
Geethanjali Engineering College
India
K. N.
Murty
Department of Applied Mathematics
Andhra University
India
nkanuri@hotmail.com
Linear Systems
time scale dynamical systems
control systems
concurrency control
Article.3.pdf
[
[1]
B. Aulbach, S. Hilger, A unified Approach to Continuous and Discrete Dynamics, Qualitative theory of differential equations (Szeged), 1988 (1988), 37-56
##[2]
B. Aulbach, S. Hilger, Linear dynamic processes with inhomogeneous time scale, Nonlinear dynamics and quantum dynamical systems (Gaussig), 1990 (1990), 9-20
##[3]
M. Bohner, A. Peterson, Dynamic Equations on Time Scales, Birkhäuser, Boston (2001)
##[4]
M. Bohner, A. Peterson, Advances in Dynamics Equations on Time Scales, Birkhäuser, Boston (2003)
##[5]
K. V. V. Kanuri, , R. Suryanarayana, K. N. Murty, Existence of $\Psi$-bounded solutions for linear differential systems on time scales, J. Math. Comput. Sci., 20 (2020), 1-13
##[6]
V. Lakshmikantham, S. Sivasundaram, B. Kaymakcalan, Dynamic systems on measure chains, Kluwer Academic Publishers Group, Dordrecht (1996)
##[7]
H. J. Ko, Stability Analysis of Digital Filters Under Finite Word Length Effects via Normal-Form Transformation, Asian J. Health Infor. Sci., 1 (2006), 112-121
##[8]
K. N. Murty, Y. Wu, V. Kanuri, Metrics that suit for dichotomy, well conditioning and object oriented design on measure chains, Nonlinear Stud., 18 (2011), 621-637
]
Some fixed point theorems in fuzzy bipolar metric spaces
Some fixed point theorems in fuzzy bipolar metric spaces
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en
In this paper, we introduce the notion of fuzzy bipolar metric space and prove some fixed point results in this space. We provide some non-trivial examples to support our claim and also give applications for the usability of the main result in fuzzy bipolar metric spaces.
196
204
Ayush
Bartwal
Department of Mathematics
HNB Garhwal University
India
ayushbartwal@gmail.com
R. C.
Dimri
Department of Mathematics
HNB Garhwal University
India
dimrirc@gmail.com
Gopi
Prasad
Department of Mathematics
HNB Garhwal University
India
gopiprasad127@gmail.com
Fuzzy metric spaces
fuzzy bipolar metric space
fixed point
Article.4.pdf
[
[1]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399
##[2]
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389
##[3]
V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252
##[4]
V. Gupta, N. Mani, A. Saini, Fixed point theorems and its applications in fuzzy metric spaces, Conference Paper, 2013 (2013), 1-11
##[5]
G. N. V. Kishore, R. P. Agarwal, B. Srinuvasa Rao, R. V. N. Srinuvasa Rao, Caristi type cyclic contraction and common fixed point theorems in bipolar metric spaces with applications, Fixed Point Theory Appl., 2018 (2018), 1-13
##[6]
I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), 326-334
##[7]
D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, 144 (2004), 431-439
##[8]
S. N. Mishra, N. Sharma, S. L. Singh, Common fixed points of maps on fuzzy metric spaces, Internat. J. Math. Math. Sci., 17 (1994), 253-258
##[9]
A. Mutlu, U. Gürdal, Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl., 9 (2016), 5362-5373
##[10]
A. Mutlu, K. Özkan, U. Gürdal, Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure Appl. Math., 10 (2017), 655-667
##[11]
A. Mutlu, K. Özkan, U. Gürdal, Fixed point theorems for multivalued mapping on bipolar metric spaces, Fixed Point Theory, (), -
##[12]
A. Mutlu, K. Özkan, U. Gürdal, Locally and weakly contractive principle in bipolar metric spaces, TWMS J. App. Eng. Math., (), -
##[13]
B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334
##[14]
L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353
]