Benchohra M. Fractional Differential Equations. New Advancements...2023 torrent

Textbook in PDF format

This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.
Preface
Introduction
Preliminary Background
Notations and Functional Spaces
Space of Continuous Functions
Spaces of Integrable Functions
Spaces of Continuous Functions with Weight
Special Functions of the Fractional Calculus
Gamma Function
k-Gamma and k-Beta Functions
Elements from Fractional Calculus Theory
Fractional Integrals
Fractional Derivatives
Necessary Lemmas, Theorems and Properties
Kuratowski Measure of Noncompactness
Fixed Point Theorems
Hybrid Fractional Differential Equations
Introduction and Motivations
Initial Value Problem for Hybrid Generalized Hilfer Fractional Differential Equations
Introduction
Existence Results
Examples
Boundary Value Problem for Hybrid Generalized Hilfer Fractional …
Introduction
Existence Results
Examples
Nonlocal Initial Value Problem for Hybrid Generalized Hilfer-type …
Existence Results
Examples
Notes and Remarks
Fractional Differential Equations with Retardation and Anticipation
Introduction and Motivations
On k-Generalized ψ-Hilfer Boundary Value …
Existence Results
Examples
Nonlocal k-Generalized ψ-Hilfer Terminal Value Problem …
Existence Results
Examples
Notes and Remarks
Impulsive Fractional Differential Equations with Retardation and Anticipation
Introduction and Motivations
On k-Generalized ψ-Hilfer Impulsive Boundary Value …
Existence Results
An Example
On k-Generalized ψ-Hilfer Impulsive Boundary Value Problem …
Existence Results
An Example
Nonlocal k-Generalized ψ-Hilfer Impulsive Initial …
Existence Results
An Example
Notes and Remarks
Coupled Systems for Fractional Differential Equations
Introduction and Motivations
On Coupled Systems for k-Generalized ψ-Hilfer …
Existence Results
An Example
Implicit Coupled k-Generalized …
Existence Results
An Example
Notes and Remarks
Bibliography
Index