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yong z basic theory fractional differential equations 3ed 2023

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Textbook in PDF format 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 Rayleigh–Stokes equations, and wave equations. The bibliography has also been updated and expanded. Preface to the Third Edition About the Author Preliminaries Introduction Some Notations, Concepts and Lemmas Fractional Calculus Definitions Properties Mittag-Leffler Functions Some Results from Nonlinear Analysis Laplace and Fourier Transforms Sobolev Spaces Measure of Noncompactness Topological Degree Picard Operator Fixed Point Theorems Critical Point Theorems Semigroups C-Semigroup Almost Sectorial Operators Fractional Functional Differential Equations Introduction Neutral Equations with Bounded Delay Introduction Existence and Uniqueness Extremal Solutions p-Type Neutral Equations Introduction Existence and Uniqueness Continuous Dependence Neutral Equations with Infinite Delay Introduction Existence and Uniqueness Continuation of Solutions Iterative Functional Differential Equations Introduction Existence Data Dependence Examples and General Cases Oscillations and Nonoscillations Introduction Preliminaries Oscillation of Neutral Differential Systems Existence of Nonoscillatory Solutions Fractional Partial Functional Differential Equations Oscillation of Fractional ODEs Boundary Value Problem Example Notes and Remarks Fractional Ordinary Differential Equations in Banach Spaces Introduction Cauchy Problems via Measure of Noncompactness Method Introduction Existence Cauchy Problems via Topological Degree Method Introduction Qualitative Analysis Cauchy Problems via Picard Operators Technique Introduction Results via Picard Operators Results via Weakly Picard Operators Notes and Remarks Fractional Abstract Evolution Equations Introduction Evolution Equations with Riemann-Liouville Derivative Introduction Definition of Mild Solutions Preliminary Lemmas Compact Semigroup Case Noncompact Semigroup Case Evolution Equations with Caputo Derivative Introduction Definition of Mild Solutions Preliminary Lemmas Compact Semigroup Case Noncompact Semigroup Case Nonlocal Problems for Evolution Equations IntroductionThe nonlocal condition has a Definition of Mild Solutions Existence Optimal Controls of Fractional Evolution Equations Introduction Preliminaries Existence of α-Mild Solutions Existence of Fractional Optimal Controls Abstract Cauchy Problems with Almost Sectorial Operators Introduction Properties of Operators Linear Problems Nonlinear Problems Applications Evolution Equations with Hilfer Derivative Introduction Preliminaries Some Lemmas Existence Results Infinite Interval Problems with Hilfer Derivative Introduction Preliminaries Lemmas Existence on Infinite Interval Notes and Remarks Fractional Impulsive Differential Equations Introduction Impulsive Initial Value Problems Introduction Formula of Solutions Existence Impulsive Boundary Value Problems Introduction Formula of Solutions Existence Impulsive Langevin Eq IntroductionIn 1908, Langevin introduced Formula of Solutions Existence Impulsive Evolution Equations Introduction Cauchy Problems Nonlocal Problems Notes and Remarks Fractional Boundary Value Problems Introduction Solutions for BVP with Left and Right Fractional Integrals Introduction Fractional Derivative Space Variational Structure Existence under Ambrosetti-Rabinowitz Con Superquadratic Case Asymptotically Quadratic Case Multiple Solutions for BVP with Parameters Introduction Existence Infinite Solutions for BVP with Left and Right Fractional Integrals Introduction Existence Solutions for BVP with Left and Right Fractional Derivatives Introduction Variational Structure Existence of Weak Solutions Existence of Solutions Notes and Remarks Fractional Hamiltonian Systems Introduction Existence and Multiplicity of Homoclinic Solutions (I) Fractional Derivative Space Some Lemmas Existence of Homoclinic Solutions Existence and Multiplicity of Homoclinic Solutions (II) Introduction Some Lemmas Existence and Multiplicity Notes and Remarks Fractional Partial Differential Equations Introduction Fractional Navier-Stokes Equations Introduction Preliminaries Global Existence Local Existence Regularity Fractional Rayleigh-Stokes Equations Introduction Preliminaries Space Settings Solution Representation Globally Lispchitz Source Term Locally Lispchitz Source Term Existence of the Mild Solution Continuation and Blow-Up Alternative Fractional Euler-Lagrange Equations Introduction Functional Spaces Variational Structure Existence of Weak Solution Fractional Diffusion Equations Introduction Regularity and Unique Existence Fractional Wave Equations Introduction Preliminaries Approximation Solution Energy Estimates Well-Posedness and Regularity Notes and Remarks Bibliography Index

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yong z basic theory fractional differential equations 3ed 2023

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