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

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

Autorentext

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 functional analysis and metric fixed point theory. Mouffak Benchohra, Ph.D., is a Full Professor in the Department of Mathematics at Djillali Liabes University of Sidi Bel Abbes. Dr. Benchohra received a master's degree in Nonlinear Analysis from Tlemcen University, and a Ph.D. in Mathematics from Djillali Liabes University, Sidi Bel Abbes. His research fields include fractional differential equations, evolution equations and inclusions, and control theory and applications. He has published more than 500 papers and five monographs. He has also occupied the position of head of department of mathematics at Djillali Liabes University, Sidi Bel Abbes. Dr. Benchohra is on the Editorial Board of 10 international journals. Jamal Eddine Lazreg, Ph.D., is a Full Professor in the Department of Mathematics at Djillali Liabes University of Sidi Bel Abbes. Dr. Lazreg received a master's degree in functional analysis from Djillali Liabes University and a Ph.D. in differential equations from Djillali Liabes University of Sidi Bel Abbes. His research fields include fractional differential equations and inclusions. Abdelrkim Salim, Ph.D., is an Associate Professor of Technology at Hassiba Benbouali University of Chlef. Dr. Salim received a master's degree in functional analysis and differential equations from Djillali Liabès University and a Ph.D. in mathematical analysis and applications from Djillali Liabes University of Sidi Bel Abbes. His research fields include fractional differential equations and inclusions, and control theory and applications.

Inhalt

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