Advanced Topics in Fractional Differential Equations: A Fixed Point Approach [Hardcover]

This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers understanding of the concepts presented.

 Includes illustrations in order to support readers understanding of the presented concepts

?         Approaches the topic of fractional differential equations while employing fixed point theorems as tools

?         Presents novel results, which build upon previous literature and many years of research by the authors

Introduction.- Preliminary Background.- Implicit Fractional Differential Equations.- Fractional Differential Equations with Instantaneous Impulses.- Fractional Differential Equations with Non-Instantaneous Impulses.

Erdal Karapinar, Ph.D., is a Professor in the Department of Mathematics at Cankaya University and Visiting Professor at the China Medical University of Taichung. He completed his Ph.D. at the Middle East Technical University (METU), Turkiye, in 2004. He has written more than 400 research articles in peer reviewed journals. His research interests include functil,