Basic theory of fractional differential equations / Yong Zhou.

Format:

Book

Author/Creator:

Zhou, Yong, 1964- author.

Language:

English

Subjects (All):

Fractional differential equations.

Physical Description:

1 online resource (304 p.)

Place of Publication:

Singapore : World Scientific, 2014.

Language Note:

English

Summary:

This invaluable book is devoted to a rapidly developing area on the research of the qualitative theory of fractional differential equations. It is self-contained and unified in presentation, and provides readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the Picard operators technique, critical point theory and semigroups theory. Based on research work carried

Contents:

Preface; Contents; 1. Preliminaries; 1.1 Introduction; 1.2 Some Notations, Concepts and Lemmas; 1.3 Fractional Calculus; 1.3.1 Definitions; 1.3.2 Properties; 1.4 Some Results from Nonlinear Analysis; 1.4.1 Sobolev Spaces; 1.4.2 Measure of Noncompactness; 1.4.3 Topological Degree; 1.4.4 Picard Operator; 1.4.5 Fixed Point Theorems; 1.4.6 Critical Point Theorems; 1.5 Semigroups; 1.5.1 C0-Semigroup; 1.5.2 Almost Sectorial Operators; 2. Fractional Functional Differential Equations; 2.1 Introduction; 2.2 Neutral Equations with Bounded Delay; 2.2.1 Introduction; 2.2.2 Existence and Uniqueness

2.2.3 Extremal Solutions2.3 p-Type Neutral Equations; 2.3.1 Introduction; 2.3.2 Existence and Uniqueness; 2.3.3 Continuous Dependence; 2.4 Neutral Equations with Infinite Delay; 2.4.1 Introduction; 2.4.2 Existence and Uniqueness; 2.4.3 Continuation of Solutions; 2.5 Iterative Functional Differential Equations; 2.5.1 Introduction; 2.5.2 Existence; 2.5.3 Data Dependence; 2.5.4 Examples and General Cases; 2.6 Notes and Remarks; 3. Fractional Ordinary Differential Equations in Banach Spaces; 3.1 Introduction; 3.2 Cauchy Problems via Measure of Noncompactness Method; 3.2.1 Introduction

3.2.2 Existence3.3 Cauchy Problems via Topological Degree Method; 3.3.1 Introduction; 3.3.2 Qualitative Analysis; 3.4 Cauchy Problems via Picard Operators Technique; 3.4.1 Introduction; 3.4.2 Results via Picard Operators; 3.4.3 Results via Weakly Picard Operators; 3.5 Notes and Remarks; 4. Fractional Abstract Evolution Equations; 4.1 Introduction; 4.2 Evolution Equations with Riemann-Liouville Derivative; 4.2.1 Introduction; 4.2.2 Definition of Mild Solutions; 4.2.3 Preliminary Lemmas; 4.2.4 Compact Semigroup Case; 4.2.5 Noncompact Semigroup Case

4.3 Evolution Equations with Caputo Derivative4.3.1 Introduction; 4.3.2 Definition of Mild Solutions; 4.3.3 Preliminary Lemmas; 4.3.4 Compact Semigroup Case; 4.3.5 Noncompact Semigroup Case; 4.4 Nonlocal Cauchy Problems for Evolution Equations; 4.4.1 Introduction; 4.4.2 Definition of Mild Solutions; 4.4.3 Existence; 4.5 Abstract Cauchy Problems with Almost Sectorial Operators; 4.5.1 Introduction; 4.5.2 Preliminaries; 4.5.3 Properties of Operators; 4.5.4 Linear Problems; 4.5.5 Nonlinear Problems; 4.5.6 Applications; 4.6 Notes and Remarks

5. Fractional Boundary Value Problems via Critical Point Theory5.1 Introduction; 5.2 Existence of Solution for BVP with Left and Right Fractional Integrals; 5.2.1 Introduction; 5.2.2 Fractional Derivative Space; 5.2.3 Variational Structure; 5.2.4 Existence under Ambrosetti-Rabinowitz Condition; 5.2.5 Superquadratic Case; 5.2.6 Asymptotically Quadratic Case; 5.3 Multiple Solutions for BVP with Parameters; 5.3.1 Introduction; 5.3.2 Existence; 5.4 Infinite Solutions for BVP with Left and Right Fractional Integrals; 5.4.1 Introduction; 5.4.2 Existence

5.5 Existence of Solutions for BVP with Left and Right Fractional Derivatives

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

981-4579-90-4