Basic Theory Of Fractional Differential Equations

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 out by the author and other experts during the past four years, the contents are very new and comprehensive. It is useful to researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines.
Contents:Preliminaries:IntroductionSome Notations, Concepts and LemmasFractional CalculusSome Results from Nonlinear AnalysisSemigroupsFractional Functional Differential Equations:IntroductionNeutral Equations with Bounded Delayp-Type Neutral EquationsNeutral Equations with Infinite DelayIterative Functional Differential EquationsNotes and RemarksFractional Ordinary Differential Equations in Banach Spaces:IntroductionCauchy Problems via Measure of Noncompactness MethodCauchy Problems via Topological Degree MethodCauchy Problems via Picard Operators TechniqueNotes and RemarksFractional Abstract Evolution Equations:IntroductionEvolution Equations with Riemann-Liouville DerivativeEvolution Equations with Caputo DerivativeNonlocal Cauchy Problems for Evolution EquationsAbstract Cauchy Problems with Almost Sectorial OperatorsNotes and RemarksFractional Boundary Value Problems via Critical Point Theory:IntroductionExistence of Solution for BVP with Left and Right Fractional IntegralsMultiple Solutions for BVP with ParametersInfinite Solutions for BVP with Left and Right Fractional IntegralsExistence of Solutions for BVP with Left and Right Fractional DerivativesNotes and RemarksFractional Partial Differential Equations:IntroductionFractional Euler-Lagrange EquationsTime-Fractional Diffusion EquationsFractional Hamiltonian SystemsFractional Schrödinger EquationsNotes and Remarks
Readership: Graduate students and researchers in the fields of fractional differential equations, fractional calculus and related areas of research.