本书主要介绍分数阶扩散方程解的存在性、正则性和稳定性。本书的主要内容来自作者近年来的研究成果，分为四章。第一章介绍了分数阶微积分、非线性分析和算子半群等基本知识。第二章介绍了一些分数阶扩散方程初值（或边值）问题解的存在性结果。第三章的主要目的是介绍分数阶扩散方程有界解（如周期解）的存在性。第四章研究分数自治（或非自治）扩散方程解的存在性和正则性。

《博士后文库》序言
Preface
Chapter 1 Preliminaries
1.1 Introduction
1.2 Fractionalintegrals and fractional derivatives
1.3 Mittag-Leffler functions
1.4 Measureof noncompactness
1.5 Semigroupsofoperators
1.6 Fixedpointtheorems
1.7 Definitions of solutions to abstract fractional equations
1.8 Other lemmas
Chapter 2 Initial (or Boundary)Value Problems forFractional Diffusion Equations
2.1 Impulsive fractional diffusion equations with nonlocal initial conditions
2.1.1 Introduction
2.1.2 Existence of mild solutions
2.1.3 Examples
2.1.4 Notes and remarks
2.2 Initial problems for fractional diffusion equations in fractionalpower spaces
I2.2.1 ntroduction
2.2.2 Existence of q-mild solutions
2.2.3 Existence of q-classical solutions
2.2.4 Applications
2.2.5 Notes and remarks
2.3 Positive mild solutionstoperiodicboundaryvalue problemsfor fractional diffusion equations 32 Introduction
2.3.1 Contents
2.3.2 Existence of mild solutions
2.3.3 Examples
2.3.4 Notes and remarks
2.4 Periodicboundaryvalue problems for semilinear fractional differential equations
2.4.1 Introduction
2.4.2 Existence of mild solutions
2.4.3 Notes and remarks
Chapter 3 Bounded Solutions toFractional Diffusion Equations
3.1 Bounded solutions to fractional diffusion equations with C0-semigroups
3.1.1 Introduction
3.1.2 Results for linear equations
3.1.3 Results for nonlinear equations
3.1.4 Examples
3.1.5 Notes and remarks
3.2 Periodic (orS-asymptotically) solutions to fractional diffusion equations in fractionalpower spaces
3.2.1 Introduction
3.2.2 Existenceofperiodic(or S-asymptotically) mild or classical solutions
3.2.3 Examples
3.2.4 Notes and remarks
3.3 Square-mean S-asymptoticallyperiodic solutions to fractional stochastic diffusion equations
3.3.1 Introduction
3.3.2 Existence-uniqueness of square-mean S-asymptotically !-periodic solutions
3.3.3 Asymptotically stabilityof square-mean S-asymptotically !-periodic solutions
3.3.4 Examples
3.3.5 Notes and remarks
Chapter 4 Existence and Regularityof Solutions toFractional Diffusion Equations
4.1 Existence and regularityof solutions to fractional diffusion equations involving time-dependentdiffusion coefficients
4.1.1 Introduction
4.1.2 Existence and regularityof classical solutions
4.1.3 Notes and remarks
4.2 Existence and regularityof solutions to fractional diffusion equations involving time-space-dependent diffusion coefficients
4.2.1 Introduction
4.2.2 Existence and regularityof classical solutions
4.2.3 Notes and remarks
Bibliography
Index
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