Basic Theory of Fractional Differential Equations
2nd Edition

By (author): Yong Zhou (Xiangtan University, China), JinRong Wang (Guizhou University, China), Lu Zhang (Xiangtan University, China)



This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations. It provides the 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 technique of Picard operators, critical point theory and semigroup theory. Based on the research work carried out by the authors and other experts during the past seven years, the contents are very recent and comprehensive.

In this edition, two new topics have been added, that is, fractional impulsive differential equations, and fractional partial differential equations including fractional Navier–Stokes equations and fractional diffusion equations.

Contents:

Preliminaries:
• Introduction
• Some Notations, Concepts and Lemmas
• Fractional Calculus
• Some Results from Nonlinear Analysis
• Semigroups

Fractional Functional Differential Equations:
• Introduction
• Neutral Equations with Bounded Delay
• p-Type Neutral Equations
• Neutral Equations with Infinite Delay
• Iterative Functional Differential Equations
• Notes and Remarks

Fractional Ordinary Differential Equations in Banach Spaces:
• Introduction
• Cauchy Problems via Measure of Noncompactness Method
• Cauchy Problems via Topological Degree Method
• Cauchy Problems via Picard Operators Technique
• Notes and Remarks

Fractional Abstract Evolution Equations:
• Introduction
• Evolution Equations with Riemann–Liouville Derivative
• Evolution Equations with Caputo Derivative
• Nonlocal Problems for Evolution Equations
• Abstract Cauchy Problems with Almost Sectorial Operators
• Notes and Remarks

Fractional Impulsive Differential Equations:
• Introduction
• Impulsive Initial Value Problems
• Impulsive Boundary Value Problems
• Impulsive Langevin Equations
• Impulsive Evolution Equations
• Notes and Remarks

Fractional Boundary Value Problems:
• Introduction
• Solution for BVP with Left and Right Fractional Integrals
• Multiple Solutions for BVP with Parameters
• Infinite Solutions for BVP with Left and Right Fractional Integrals
• Solutions for BVP with Left and Right Fractional Derivatives
• Notes and Remarks

Fractional Partial Differential Equations:
• Introduction
• Fractional Navier–Stokes Equations
• Fractional Euler–Lagrange Equations
• Fractional Diffusion Equations
• Fractional Schrödinger Equations
• Notes and Remarks



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