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2019
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An extension of the optimal homotopy asymptotic method with applications to nonlinear coupled partial differential equations
An extension of the optimal homotopy asymptotic method with applications to nonlinear coupled partial differential equations
en
en
In this paper, we applied an extension of optimal homotopy asymptotic method (EOHAM) for the approximate solution of coupled partial differential equations (PDEs). The obtained results are compared with other results for its efficiency. The order of convergence and residuals are plotted.
218
229
Mehreen
Fiza
Department of Mathematics
Abdul Wali Khan University
Pakistan
Farkhanda
Chohan
Department of Information Technology
Burraimi University College Burraimi
Oman
Hakeem
Ullah
Department of Mathematics
Abdul Wali Khan University
Pakistan
hakeemullah1@gmail.com
Saeed
Islam
Department of Mathematics
Abdul Wali Khan University
Pakistan
Samia
Bushnaq
Department of Basic Sciences, King Abdullah II Faculty of Engineering
Princess Sumaya University for Technology
Jordan
EOHAM
HPM
exact
coupled PDEs
Article.1.pdf
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H. Ullah, S. Islam, M. Fiza, Analytical Solution for Three-Dimensional Problem of Condensation Film on Inclined Rotating Disk by Extended Optimal Homotopy Asymptotic Method, Iran. J. Sci. Tech. Mech. Eng., 40 (2016), 265-273
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H. Ullah, S. Islam, M. Idrees, M. Arif, Solution of boundary layer problem with heat transfer by optimal homotopy asymptotic method, Abstr. Appl. Anal., 2013 (2013), 1-10
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H. Ullah, S. Islam, M. Idrees, M. Fiza, Solution of the differential-difference equations by optimal homotopy asymptotic method, Abstr. Appl. Anal., 2014 (2014), 1-7
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H. Ullah, S. Islam S, M. Idrees, R. Nawaz, Application of Optimal Homotopy Asymptotic Method to Doubly Wave Solutions of the Coupled Drinfel'd-Sokolov-Wilson Equations, Math. Probl. Eng., 2013 (2013), 1-8
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H. Ullah, S. Islam, I. Khan, S. Shafie, M. Fiza, Formulation and Applications of Optimal Homotopy Asymptotic Method to Coupled Differential-Difference Equations, PlosOne, 2015 (2015), 1-14
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]
Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for \(p\)-convex functions via new fractional conformable integral operators
Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for \(p\)-convex functions via new fractional conformable integral operators
en
en
In this paper, we obtained the Hermite-Hadamard and
Hermite-Hadamard-Fejer type inequalities for \(p\)-convex functions
via new fractional conformable integral operators. We also gave some
new Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities
for convex functions and harmonically convex functions via new
fractional conformable integral operators.
230
240
Naila
Mehreen
School of Natural Sciences
National University of Sciences and Technology
Pakistan
nailamehreen@gmail.com
Matloob
Anwar
School of Natural Sciences
National University of Sciences and Technology
Pakistan
Hermite-Hadamard inequalities
Hermite-Hadamard-Fejer inequalities
Riemann-Liouville fractional integral
fractional conformable integral operators
convex functions
\(p\)-convex functions
harmonically convex functions
Article.2.pdf
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I. Işcan, Hermite-Hadamard type inequalities for $p$-convex functions, Int. J. Anal. Appl., 11 (2016), 137-145
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Geometric meaning of conformable derivative via fractional cords
Geometric meaning of conformable derivative via fractional cords
en
en
In this paper, we answer the question
that many researchers did ask us about: "what is the geometrical
meaning of the conformable derivative?". We answer the question
using the concept of fractional cords. Fractional orthogonal
trajectories are also introduced. Some examples illustrating the
concepts of fractional cords and fractional orthogonal trajectories
are given.
241
245
Roshdi
Khalil
Department of Mathematics
The University of Jordan
Jordan
roshdi@ju.edu.jo
Mohammed
AL Horani
Department of Mathematics
The University of Jordan
Jordan
horani@ju.edu.jo
Mamon
Abu Hammad
Department of Mathematics
Zaytoonah University
Jordan
m.abuhammad@zuj.edu.jo
Fractional derivatives
fractional cords
orthogonal fractional trajectory
Article.3.pdf
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[1]
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66
##[2]
M. Abu Hammad, R. Khalil, Abel's formula and Wronskian for conformable fractional differential equations, Int. J. Differ. Equ. Appl., 13 (2014), 177-183
##[3]
M. Abu Hammad, R. Khalil, Conformable fractional heat differential equation, Int. J. Pure. Appl. Math., 94 (2014), 215-221
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam (2006)
]
Straddles on ternary semigroups
Straddles on ternary semigroups
en
en
A ternary semigroup is a nonempty set with a ternary operation satisfy the associative law. In this paper, we define straddles on ternary semigroups and investigate some properties of straddles of ternary semigroups.
246
250
Phoschanun
Ratanaburee
Department of Mathematics and Statistics, Faculty of Science
Prince of Songkla University
Thailand
Thananya
Kaewnoi
Department of Mathematics and Statistics, Faculty of Science
Prince of Songkla University
Thailand
Ronnason
Chinram
Department of Mathematics and Statistics, Faculty of Science
Centre of Excellence in Mathematics
Prince of Songkla University
CHE
Thailand
Thailand
ronnason.c@psu.ac.th
Straddles
ternary semigroups
commutative elements
homomorphisms
Article.4.pdf
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[1]
M. Y. Abbasi, S. A. Khan, On some generalized ideals in ternary semigroups, Quasigroups Related Systems, 25 (2017), 181-188
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M. A. Ansari, N. Yaqoob, T-rough ideals in ternary semigroups, Int. J. Pure Appl. Math., 86 (2013), 411-424
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N. Yaqoob, M. Khan, M. Akram, A. Khan, Interval valued intuitionistic $(\overline{s}, \overline{t})$-fuzzy ideals of ternary semigroups, Indian J. Sci. Technol., 6 (2013), 5418-5428
]
A note on likelihood ratio ordering between parallel systems with two exponential components
A note on likelihood ratio ordering between parallel systems with two exponential components
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en
With the aid of computer programming, we obtain a result on stochastic comparison of the lifetime of two parallel systems with two exponential components in terms of likelihood ratio ordering. This result reveals a more comprehensive picture on stochastic ordering between parallel systems and
thus provides a relatively satisfied answer to an open problem raised in [N. Balakrishnan, P. Zhao, Probab. Engrg. Inform. Sci., \(\bf 27\) (2013), 403--443].
251
257
Emanuel
Emanouilidis
School of Computer Science
Kean University
USA
eemanoui@kean.edu
Jiantian
Wang
School of Mathematical Science
Kean University
USA
jwang@kean.edu
Parallel system
stochastic comparison
likelihood ratio order
Article.5.pdf
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[1]
N. Balakrishnan, P. Zhao, Ordering properties of order statistics from heterogeneous populations: a review with an emphasis of some recent developments, Probab. Engrg. Inform. Sci., 27 (2013), 403-443
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M. Shaked, J. G. Shanthikumar, Stochastic Orders, Springer, New York (2007)
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R. F. Yan, G. F. Da, P. Zhao, Further Results for Parallel Systems with Two Heterogeneous Exponential Components, Statistics, 47 (2013), 1128-1140
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P. Zhao, N. Balakrishnan, Some characterization results for parallel systems with two heterogeneous exponential components, Statistics, 45 (2011), 593-604
]
A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology
A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology
en
en
In this study, we have explored the approximate solution of \(2^{nd}\) order singular boundary value problems (SBVP's) using extended cubic B-spline (ECBS) collocation approach. The accuracy of the numerical algorithm has been enhanced by means of a novel ECBS approximation for $2^{nd}$ order derivative. To endorse our claim, few test examples have been considered and the experimental results are compared with the already existing methods. It is observed that the proposed technique is more accurate and efficient in comparison to the existing techniques on the topic.
258
267
Imtiaz
Wasim
Department of Mathematics
University of Sargodha
Pakistan
Muhammad
Abbas
Department of Mathematics
University of Sargodha
Pakistan
Muhammad Kashif
Iqbal
Department of Mathematics,
Government College University
Pakistan
kashifiqbal@gcuf.edu.pk
Singular boundary value problems
extended B-spline functions
quasi-linearization technique
extended B-spline collocation method
Article.6.pdf
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M. Abukhaled, S. A. Khuri, A. Sayfy, A numerical approach for solving a class of singular boundary value problems arising in physiology, Int. J. Numer. Anal. Model., 8 (2011), 353-363
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]
An improvement of Laguerre computational scheme for solving nonlinear age-structured population models
An improvement of Laguerre computational scheme for solving nonlinear age-structured population models
en
en
In this paper, we simultaneously implement two kinds of orthogonal polynomials for solving a nonlinear age-structured population model. This non-classic type of partial differential equation is typically defined in large domains that makes finding an accurate solution by common techniques to be difficult. The presented method namely modified generalized Laguerre-Chebyshev (MGLC), which is based on the modified generalized Laguerre functions and Chebyshev orthogonal polynomials provides the spectral accuracy. The theoretical and experimental analysis of the scheme reliability verifies the validity of the proposed method in large domains.
268
287
Zakieh
Avazzadeh
School of Mathematical Sciences
Nanjing Normal University
China
z.avazzadeh@njnu.edu.cn
Mohammad
Heydari
Department of Mathematics
Yazd University
Iran
Shantia
Yarahmadian
Mississippi State University
United States
Nonlinear age-structured population model
generalized Laguerre functions
modified generalized Laguerre functions
orthogonal polynomials
error analysis
Article.7.pdf
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S. Abbasbandy, E. Shivanian, Numerical simulation based on meshless technique to study the biological population model, Math. Sci., 10 (2016), 123-130
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Z. Avazzadeh, M. Heydari, Chebyshev cardinal functions for solving age-structured population models, Int. J. Appl. Comput. Math., 3 (2017), 2139-2149
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Z. Avazzadeh, M. Heydari, Haar wavelet method for solving nonlinear age-structured population models, Int. J. Biomath., 10 (2017), 1-21
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