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ABOUT THE BOOK

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

TABLE OF CONTENTS

1. Introduction

   • Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg, Abdelkrim Salim

   Pages 1-8

2. Preliminary Background

   • Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg, Abdelkrim Salim

   Pages 9-34

3. Implicit Fractional Differential Equations

   • Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg, Abdelkrim Salim

   Pages 35-76

4. Fractional Differential Equations with Instantaneous Impulses

   • Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg, Abdelkrim Salim

   Pages 77-116

5. Fractional Differential Equations with Non-Instantaneous Impulses

   • Mouffak Benchohra, Erdal Karapınar, Jamal Eddine Lazreg, Abdelkrim Salim

   Pages 117-168