Table Of Content

Applied Mathematics and Fractional Calculus Edited by Francisco Martínez González 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 Mart´ınez Gonza´lez Mohammed K. A. Kaabar (cid:13) (cid:13) (cid:13) (cid:13) (cid:13) (cid:13) (cid:13) (cid:13) (cid:13) MDPI Basel Beijing Wuhan Barcelona Belgrade Manchester Tokyo Cluj Tianjin Editors FranciscoMart´ınezGonza´lez MohammedK.A.Kaabar DepartamentodeMatema´tica InstituteofMathematical AplicadayEstad´ıstica Sciences,FacultyofScience UniversidadPolite´cnicade UniversitiMalaya, Cartagena KualaLumpur50603 Cartagena Malaysia Spain EditorialOffice MDPI St. Alban-Anlage66 4052Basel,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/special issues/ Applied Mathematics Fractional Calculus). For citation purposes, cite each article independently as indicated on the article page online and as indicatedbelow: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Volume Number, PageRange. ISBN978-3-0365-5148-7(Hbk) ISBN978-3-0365-5147-0(PDF) © 2022 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon publishedarticles,aslongastheauthorandpublisherareproperlycredited,whichensuresmaximum disseminationandawiderimpactofourpublications. ThebookasawholeisdistributedbyMDPIunderthetermsandconditionsoftheCreativeCommons licenseCCBY-NC-ND. Contents AbouttheEditors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Prefaceto”AppliedMathematicsandFractionalCalculus” . . . . . . . . . . . . . . . . . . . . . xi Mohammad Esmael Samei, Rezvan Ghaffari, Shao-Wen Yao, Mohammed K. A. Kaabar, FranciscoMart´ınezandMustafaInc Existence of Solutions for a Singular Fractional q-Differential [-25]Equations under Riemann–LiouvilleIntegralBoundaryCondition Reprintedfrom: Symmetry2021,13,1235,doi:10.3390/sym13071235 . . . . . . . . . . . . . . . . . 1 MalgorzataKlimek Spectrum of Fractional and Fractional Prabhakar Sturm–Liouville Problems with HomogeneousDirichletBoundaryConditions Reprintedfrom: Symmetry2021,13,2265,doi:10.3390/sym13122265 . . . . . . . . . . . . . . . . . 21 YuriLuchko GeneralFractionalIntegralsandDerivativesofArbitraryOrder Reprintedfrom: Symmetry2021,13,755,doi:10.3390/sym13050755 . . . . . . . . . . . . . . . . . 43 JehadAlzabut,A.GeorgeMariaSelvam,R.DhineshbabuandMohammedK.A.Kaabar The Existence, Uniqueness, and Stability Analysis of the Discrete Fractional Three-Point BoundaryValueProblemfortheElasticBeamEquation Reprintedfrom: Symmetry2021,13,789,doi:10.3390/sym13050789 . . . . . . . . . . . . . . . . . 57 ChenkuanLiandJoshuaBeaudin UniquenessofAbel’sIntegralEquationsoftheSecondKindwithVariableCoefficients Reprintedfrom: Symmetry2021,13,1064,doi:10.3390/sym13061064 . . . . . . . . . . . . . . . . . 75 Shahram Rezapour, Atika Imran, Azhar Hussain, Francisco Mart´ınez, Sina Etemad and MohammedK.A.Kaabar Condensing Functions and Approximate Endpoint Criterion for the Existence Analysis of QuantumIntegro-DifferenceFBVPs Reprintedfrom: Symmetry2021,13,469,doi:10.3390/sym13030469 . . . . . . . . . . . . . . . . . 87 AlbertoCabada,NikolayD.DimitrovandJaganMohanJonnalagadda Non-Trivial Solutions of Non-Autonomous Nabla Fractional Difference Boundary Value Problems Reprintedfrom: Symmetry2021,13,1101,doi:10.3390/sym13061101 . . . . . . . . . . . . . . . . . 109 MariaAlessandraRagusaandFanWu Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces Reprintedfrom: Symmetry2021,13,625,doi:10.3390/sym13040625 . . . . . . . . . . . . . . . . . 125 MichaelA.AwuyaandDervisSubasi Aboodh Transform Iterative Method for Solving Fractional Partial Differential Equation with Mittag–LefflerKernel Reprintedfrom: Symmetry2021,13,2055,doi:10.3390/sym13112055 . . . . . . . . . . . . . . . . . 135 SarraGuechi,RajeshDhayal,AmarDebboucheandMuslimMalik AnalysisandOptimalControlofφ-HilferFractionalSemilinearEquationsInvolvingNonlocal ImpulsiveConditions Reprintedfrom: Symmetry2021,13,2084,doi:10.3390/sym13112084 . . . . . . . . . . . . . . . . . 155 v ManuelDuarteOrtigueiraandGabrielBengochea BilateralTemperedFractionalDerivatives Reprintedfrom: Symmetry2021,13,823,doi:10.3390/sym13050823 . . . . . . . . . . . . . . . . . 173 ShuguiKang,YouminLuandWenyingFeng λ-IntervalofTriplePositiveSolutionsforthePerturbedGelfandProblem Reprintedfrom: Symmetry2021,13,1606,doi:10.3390/sym13091606 . . . . . . . . . . . . . . . . . 187 Surang Sitho, Sina Etemad, Brahim Tellab, Shahram Rezapour, Sotiris K. Ntouyas and JessadaTariboon ApproximateSolutionsofanExtendedMulti-OrderBoundaryValueProblembyImplementing TwoNumericalAlgorithms Reprintedfrom: Symmetry2021,13,1341,doi:10.3390/sym13081341 . . . . . . . . . . . . . . . . . 199 VladimirE.Fedorov,MarinaV.PlekhanovaandElizavetaM.Izhberdeeva Initial Value Problems of Linear Equations with the Dzhrbashyan–Nersesyan Derivative in BanachSpaces Reprintedfrom: Symmetry2021,13,1058,doi:10.3390/sym13061058 . . . . . . . . . . . . . . . . . 225 ShazadShawkiAhmedandShabazJalilMohammedFaeq Bessel Collocation Method for Solving Fredholm–Volterra Integro-Fractional Differential EquationsofMulti-HighOrderintheCaputoSense Reprintedfrom: Symmetry2021,13,2354,doi:10.3390/sym13122354 . . . . . . . . . . . . . . . . . 239 TinggangZhaoandYujiangWu HermiteCubicSplineCollocationMethodforNonlinearFractionalDifferentialEquationswith Variable-Order Reprintedfrom: Symmetry2021,13,872,doi:10.3390/sym13050872 . . . . . . . . . . . . . . . . . 267 PongsakornSunthrayuth,AhmedM.Zidan,Shao-WenYao,RasoolShahandMustafaInc The Comparative Study for Solving Fractional-Order Fornberg–Whitham Equation via ρ-LaplaceTransform Reprintedfrom: Symmetry2021,13,784,doi:10.3390/sym13050784 . . . . . . . . . . . . . . . . . 297 RicardoAlmeidaandNata´liaMartins New Variational Problems with an Action Depending on Generalized Fractional Derivatives, theFreeEndpointConditions,andaRealParameter Reprintedfrom: Symmetry2021,13,592,doi:10.3390/sym13040592 . . . . . . . . . . . . . . . . . 313 SachinKumar,BaljinderKour,Shao-WenYao,MustafaIncandMohamedS.Osman Invariance Analysis, Exact Solution and Conservation Laws of (2 + 1) Dim Fractional Kadomtsev-Petviashvili(KP)System Reprintedfrom: Symmetry2021,13,477,doi:10.3390/sym13030477 . . . . . . . . . . . . . . . . . 331 Nehad Ali Shah, Yasser S. Hamed, Khadijah M. Abualnaja, Jae-Dong Chung, Rasool Shah andAdnanKhan A Comparative Analysis of Fractional-Order Kaup–Kupershmidt Equation within Different Operators Reprintedfrom: Symmetry2022,14,986,doi:10.3390/sym14050986 . . . . . . . . . . . . . . . . . 347 PshtiwanOthmanMohammed,HassenAydi,ArtionKashuri,Y.S.HamedandKhadijahM. Abualnaja Midpoint Inequalities in Fractional Calculus Defined Using Positive Weighted Symmetry FunctionKernels Reprintedfrom: Symmetry2021,13,550,doi:10.3390/sym13040550 . . . . . . . . . . . . . . . . . 371 vi SaimaRashid,AasmaKhalid,SobiaSultana,ZakiaHammouch,RasoolShahandAbdullah M.Alsharif ANovelAnalyticalViewofTime-FractionalKorteweg-DeVriesEquationsviaaNewIntegral Transform Reprintedfrom: Symmetry2021,13,1254,doi:10.3390/sym13071254 . . . . . . . . . . . . . . . . . 393 vii About the Editors FranciscoMart´ınezGonza´lez FranciscoMart´ınezisatenuredassociateprofessorattheUniversidadPolite´cnicadeCartagena, 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 differentialequations,multivariatecalculusorspecialfunctions,andthedivulgationofmathematics. MohammedK.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. KaabarisanElectedForeignMemberoftheAcademyofEngineering SciencesofUkraineandUkrainianSchoolofMiningEngineering,SeniorMemberoftheHongKong Chemical,Biological&EnvironmentalEngineeringSociety(HKCBEES),andCouncilMemberofthe InternationalEngineeringandTechnologyInstitute(IETI).Hehaspublishedmorethan100research papersindexedbyScopusandWebofScience. Hehasauthoredtwomathtextbooks,andheserved 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. Kaabariscurrentlyservingasaneditorfor21internationalscientificjournalsinappliedmathematics and engineering. He is an invited keynote speaker in scientific conferences in Hong Kong, France, Ukraine,Turkey,China,Malaysia,India,Romania,USA,Singapore,andItaly. Hisresearchinterests arefractionalcalculus,appliedanalysis,fractalcalculus,appliedmathematics,mathematicalphysics, mathematicalmodellingofinfectiousdiseases,deeplearning,andnonlinearoptimization. ix