Basic Theory of Fractional Differential Equations

This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and 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, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.

In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional RayleighStokes equations, and wave equations. The bibliography has also been updated and expanded.

This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.

Contents:

• Preface to the Third Edition
• About the Author
• Fractional Functional Differential Equations
• Fractional Ordinary Differential Equations in Banach Spaces
• Fractional Abstract Evolution Equations
• Fractional Impulsive Differential Equations
• Fractional Boundary Value Problems
• Fractional Hamiltonian Systems
• Fractional Partial Differential Equations
• Bibliography
• Index

Readership: Researchers and graduate students dealing with fractional calculus and applied analysis, differential equations and related areas for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines.
Key Features:

• There were very few books in the literature presenting systematically basic theory of fractional differential equations so far. This book provides a broad scenario of the basic theory of fractional differential equations and complements the existing literature in fractional calculus
• The author presents some new approaches such as critical point theory to study fractional Hamiltonian systems and new results on fractional evolution equations and wave equations
• The materials in this book are based on the research work done so far by the author and other experts
• The contents of the book are systematic and rich

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