Nonlinear Systems of Fractional Differential Equations
Description
This book studies the theoretical aspects for a variety of coupled fractional differential systems involving Riemann-Liouville, Caputo, ?-Riemann--Liouville, Hilfer, ?--Hilfer, Hadamard, Hilfer--Hadamard, Erdelyi--Kober, (k, ?)-Hilfer, generalized, Proportional, ?-Proportional, Hilfer--proportional, ?-Hilfer--proportional type fractional derivative operators, subject to different types of nonlocal boundary conditions. The topic of fractional differential systems is one of the hot and important topics of research as such systems appear in the mathematical modeling of physical and technical phenomena. As the book contains some recent new work on the existence theory for nonlocal boundary value problems of fractional differential systems, it is expected that it will attract the attention of researchers, modelers and graduate students who are interested in doing their research on fractional differential systems.
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Bashir Ahmad is Full Professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. He received his Ph.D. degree from Quaid-i-Azam University, Islamabad, Pakistan in 1995. His research interest includes existence theory and approximate/numerical methods for nonlinear boundary value problems involving a variety of differential equations, and applied mathematics. He was honored with "Best Researcher of King Abdulaziz University" award in 2009. He supervised several Ph.D. and M.Phil./M.Sc. students. He has published 6 books and more than 745 research articles in JCR journals. His H-index is 65. He is the Managing Editor of Bulletin of Mathematical Sciences and member of editorial boards of several journals. He has been "Highly Cited Researcher" in the category of Mathematics from 2014 to 2019 (Clarivate Analytics Database). He was the top 1% of reviewers in Mathematics on Publons for the 2018 and 2019 global Peer Review Awards. He was included in the World's Top 2% Researchers Database by Stanford University from 2019 to 2023.
Sotiris K. Ntouyas is Professor Emeritus in the Department of Mathematics of the University of Ioannina, Greece. He received his BS degree and PhD from the University of Ioannina, in 1972 and 1980, respectively. His research interests include initial and boundary value problems for differential equations and inclusions, inequalities, asymptotic behavior and controllability. More than 800 of his papers have appeared in refereed journals. He is the co-author of five books. He is a member of 21 international journals' Editorial Boards, and a reviewer for many international journals. He appears in the 2018 list, published by Clarivate Analytics, of Highly Cited Researchers, and appears in the World's Top 2% Researcher lists 2019-2023 of Stanford University Database.
Content
Preliminaries.- Coupled Multi-Point fractional differential systems.- Systems of Caputo type sequential fractional differential equations.- A coupled nonlocal system of three fractional differential equations.- Nonlocal coupled systems of fractional differential equations.- Coupled systems of nonlinear multi-term fractional differential equations.- Nonlinear mixed-order coupled fractional differential systems.- Systems of Hilfer type fractional differential equations.- Coupled systems of sequential Caputo and Hadamard fractional differential equations.- Systems of fractional Langevin equations with boundary conditions.- A system of nonlocal Erd´elyi-Kober fractional differential equations.- Positive solutions for fractional differential systems.- A Langevin-type ??-variant system.- A coupled system of fractional ??-integro-difference equations.