Applied Mathematics and Fractional Calculus

440 Pages·2021·29.691 MB·English

by  Francisco Martinez Gonzalez, Mohammed K. A. Kaabar

symmetry
Applied
Mathematics and
Fractional Calculus
Edited by
Francisco Martmez Gonzalez and Mohammed K. A. Kaabar
Printed Edition of the Special Issue Published in Symmetry
www.mdpi.com/journal/symmetry
Applied Mathematics and Fractional
Calculus

Applied Mathematics and Fractional
Calculus
Editors
Francisco Martinez Gonzalez
Mohammed K. A. Kaabar
MDPI • Basel• Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj* Tianjin
MDPI
Editors
Francisco Martinez Gonzalez Mohammed K. A. Kaabar
Departamento de Matematica Institute of Mathematical
Aplicada y Estadistica Sciences, Faculty of Science
Universidad Politecnica de Universiti Malaya,
Cartagena Kuala Lumpur 50603
Cartagena Malaysia
Spain
Editorial Office
MDPI
St. Alban-Anlage 66
4052 Basel, Switzerland
This is a reprint of articles from the Special Issue published online in the open access journal
Symmetry (ISSN 2073-8994) (available at: www.mdpi.com/journal/symmetry/speciaLissues/
Applied_Mathematics_Fractional_Calculus).
For citation purposes, cite each article independently as indicated on the article page online and as
indicated below:
LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Volume Number,
Page Range.
ISBN 978-3-0365-5148-7 (Hbk)
ISBN 978-3-0365-5147-0 (PDF)
© 2022 by the authors. Articles in this book are Open Access and distributed under the Creative
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Contents
About the Editors ............................................................................................................................................... ix
Preface to ”Applied Mathematics and Fractional Calculus” ................................................................ xi
Mohammad Esmael Samei, Rezvan Ghaffari, Shao-Wen Yao, Mohammed K. A. Kaabar,
Francisco Martinez and Mustafa Inc
Existence of Solutions for a Singular Fractional q-Differential [-25]Equations under
Riemann-Liouville Integral Boundary Condition
Reprinted from: Symmetry 2021, 13, 1235, doi:10.3390/sym13071235 ................................................... 1
Malgorzata Klimek
Spectrum of Fractional and Fractional Prabhakar Sturm-Liouville Problems with
Homogeneous Dirichlet Boundary Conditions
Reprinted from: Symmetry 2021, 13, 2265, doi:10.3390/sym13122265 ................................................... 21
Yuri Luchko
General Fractional Integrals and Derivatives of Arbitrary Order
Reprinted from: Symmetry 2021, 13, 755, doi:10.3390/sym13050755 ................................................... 43
Jehad Alzabut, A. George Maria Selvam, R. Dhineshbabu and Mohammed K. A. Kaabar
The Existence, Uniqueness, and Stability Analysis of the Discrete Fractional Three-Point
Boundary Value Problem for the Elastic Beam Equation
Reprinted from: Symmetry 2021, 13, 789, doi:10.3390/sym13050789 ................................................... 57
Chenkuan Li and Joshua Beaudin
Uniqueness of Abel’s Integral Equations of the Second Kind with Variable Coefficients
Reprinted from: Symmetry 2021, 13, 1064, doi:10.3390/sym13061064 ................................................... 75
Shahram Rezapour, Atika Imran, Azhar Hussain, Francisco Martinez, Sina Etemad and
Mohammed K. A. Kaabar
Condensing Functions and Approximate Endpoint Criterion for the Existence Analysis of
Quantum Integro-Difference FBVPs
Reprinted from: Symmetry 2021, 13, 469, doi:10.3390/sym13030469 ................................................... 87
Alberto Cabada, Nikolay D. Dimitrov and Jagan Mohan Jonnalagadda
Non-Trivial Solutions of Non-Autonomous Nabla Fractional Difference Boundary Value
Problems
Reprinted from: Symmetry 2021, 13, 1101, doi:10.3390/sym13061101 ................................................... 109
Maria Alessandra Ragusa and Fan Wu
Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz
Spaces
Reprinted from: Symmetry 2021, 13, 625, doi:10.3390/sym13040625 ................................................... 125
Michael A. Awuya and Dervis Subasi
Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with
Mittag-Leffler Kernel
Reprinted from: Symmetry 2021, 13, 2055, doi:10.3390/sym13112055 ................................................... 135
Sarra Guechi, Rajesh Dhayal, Amar Debbouche and Muslim Malik
Analysis and Optimal Control of ф-Hilfer Fractional Semilinear Equations Involving Nonlocal
Impulsive Conditions
Reprinted from: Symmetry 2021, 13, 2084, doi:10.3390/sym13112084 ................................................... 155
v
Manuel Duarte Ortigueira and Gabriel Bengochea
Bilateral Tempered Fractional Derivatives
Reprinted from: Symmetry 2021, 13, 823, doi:10.3390/sym13050823 173
Shugui Kang, Youmin Lu and Wenying Feng
А-Interval of Triple Positive Solutions for the Perturbed Gelfand Problem
Reprinted from: Symmetry 2021, 13, 1606, doi:10.3390/sym13091606 ................................................... 187
Surang Sitho, Sina Etemad, Brahim Tellab, Shahram Rezapour, Sotiris K. Ntouyas and
Jessada Tariboon
Approximate Solutions of an Extended Multi-Order Boundary Value Problem by Implementing
Two Numerical Algorithms
Reprinted from: Symmetry 2021, 13, 1341, doi:10.3390/sym13081341 199
Vladimir E. Fedorov, Marina V. Plekhanova and Elizaveta M. Izhberdeeva
Initial Value Problems of Linear Equations with the Dzhrbashyan-Nersesyan Derivative in
Banach Spaces
Reprinted from: Symmetry 2021, 13, 1058, doi:10.3390/sym13061058 225
Shazad Shawki Ahmed and Shabaz Jalil MohammedFaeq
Bessel Collocation Method for Solving Fredholm-Volterra Integro-Fractional Differential
Equations of Multi-High Order in the Caputo Sense
Reprinted from: Symmetry 2021, 13, 2354, doi:10.3390/sym13122354 239
Tinggang Zhao and Yujiang Wu
Hermite Cubic Spline Collocation Method for Nonlinear Fractional Differential Equations with
Variable-Order
Reprinted from: Symmetry 2021, 13, 872, doi:10.3390/sym13050872 267
Pongsakorn Sunthrayuth, Ahmed M. Zidan, Shao-Wen Yao, Rasool Shah and Mustafa Inc
The Comparative Study for Solving Fractional-Order Fornberg-Whitham Equation via
p-Laplace Transform
Reprinted from: Symmetry 2021, 13, 784, doi:10.3390/sym13050784 297
Ricardo Almeida and Natalia Martins
New Variational Problems with an Action Depending on Generalized Fractional Derivatives,
the Free Endpoint Conditions, and a Real Parameter
Reprinted from: Symmetry 2021, 13, 592, doi:10.3390/sym13040592 313
Sachin Kumar, Baljinder Kour, Shao-Wen Yao, Mustafa Inc and Mohamed S. Osman
Invariance Analysis, Exact Solution and Conservation Laws of (2 + 1) Dim Fractional
Kadomtsev-Petviashvili (KP) System
Reprinted from: Symmetry 2021, 13, 477, doi:10.3390/sym13030477 331
Nehad Ali Shah, Yasser S. Hamed, Khadijah M. Abualnaja, Jae-Dong Chung, Rasool Shah
and Adnan Khan
A Comparative Analysis of Fractional-Order Kaup-Kupershmidt Equation within Different
Operators
Reprinted from: Symmetry 2022, 14, 986, doi:10.3390/sym14050986 347
Pshtiwan Othman Mohammed, Hassen Aydi, Artion Kashuri, Y. S. Hamed and Khadijah M.
Abualnaja
Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry
Function Kernels
Reprinted from: Symmetry 2021, 13, 550, doi:10.3390/sym13040550 371
vi
Saima Rashid, Aasma Khalid, Sobia Sultana, Zakia Hammouch, Rasool Shah and Abdullah
M. Alsharif
A Novel Analytical View of Time-Fractional Korteweg-De Vries Equations via a New Integral
Transform
Reprinted from: Symmetry 2021, 13, 1254, doi:10.3390/sym13071254 393
vii

About the Editors
Francisco Martinez Gonzalez
Francisco Martinez is a tenured associate professor at the Universidad Politecnica de Cartagena,
Spain. He received his PhD degree in Physics from Universidad de Murcia in 1992. His research
interests include nonlinear dynamics methods and their applications, fractional calculus, fractional
differential equations, multivariate calculus or special functions, and the divulgation of mathematics.
Mohammed K. A. Kaabar
Mohammed K. A. Kaabar received all his undergraduate and graduate degrees in Applied
and Theoretical Mathematics from Washington State University (WSU), Pullman, WA, USA. Prof.
Kaabar has diverse experience in teaching, globally, and has worked as Adjunct Full Professor of
Mathematics, Math Lab Instructor, and Lecturer at various US institutions such as Moreno Valley
College, California, USA, Washington State University, Washington, USA, and Colorado Early
Colleges, Colorado, USA. Prof. Kaabar is an Elected Foreign Member of the Academy of Engineering
Sciences of Ukraine and Ukrainian School of Mining Engineering, Senior Member of the Hong Kong
Chemical, Biological & Environmental Engineering Society (HKCBEES), and Council Member of the
International Engineering and Technology Institute (IETI). He has published more than 100 research
papers indexed by Scopus and Web of Science. He has authored two math textbooks, and he served
as an invited referee for more than 300 Science, Technology, Engineering, and Mathematics (STEM)
international conferences and journals all over the world. He served as an editor for the American
Mathematical Society (AMS) Graduate Student Blog and full editor for an educational program
(Mathematics and Statistics Section) at California State University, Long Beach, CA, USA. Prof.
Kaabar is currently serving as an editor for 21 international scientific journals in applied mathematics
and engineering. He is an invited keynote speaker in scientific conferences in Hong Kong, France,
Ukraine, Turkey, China, Malaysia, India, Romania, USA, Singapore, and Italy. His research interests
are fractional calculus, applied analysis, fractal calculus, applied mathematics, mathematical physics,
mathematical modelling of infectious diseases, deep learning, and nonlinear optimization.
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