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。
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目录
- Contents
《博士后文库》序言
Preface
Chapter1 Preliminaries 1
1.1 Introduction 1
1.2 Fractionalintegrals and fractional derivatives 3
1.3 Mittag-Leffler functions 5
1.4 Measureof noncompactness 5
1.5 Semigroupsofoperators 6
1.6 Fixedpointtheorems 8
1.7 Definitions of solutions to abstract fractional equations 9
1.8 Other lemmas 11
Chapter2 Initial (or Boundary)Value Problems forFractional Diffusion Equations 13
2.1 Impulsive fractional diffusion equations with nonlocal initial conditions 13
2.1.1 Introduction 13
2.1.2 Existence of mild solutions 16
2.1.3 Examples 21
2.1.4 Notes and remarks 23
2.2 Initial problems for fractional diffusion equations in fractionalpower spaces 23
I2.2.1 ntroduction 23
2.2.2 Existence of q-mild solutions 25
2.2.3 Existence of q-classical solutions 30
2.2.4 Applications 30
2.2.5 Notes and remarks 32
2.3 Positive mild solutionstoperiodicboundaryvalue problemsfor fractional diffusion equations 32 Introduction 32
2.3.1 Contents
2.3.2 Existence of mild solutions 38
2.3.3 Examples 40
2.3.4 Notes and remarks 41
2.4 Periodicboundaryvalue problems for semilinear fractional differential equations 41
2.4.1 Introduction 41
2.4.2 Existence of mild solutions 44
2.4.3 Notes and remarks 51
Chapter3 Bounded Solutions toFractional Diffusion Equations 52
3.1 Bounded solutions to fractional diffusion equations with C0-semigroups 52
3.1.1 Introduction 52
3.1.2 Results for linear equations 59
3.1.3 Results for nonlinear equations 64
3.1.4 Examples 69
3.1.5 Notes and remarks 70
3.2 Periodic (orS-asymptotically) solutions to fractional diffusion equations in fractionalpower spaces 70
3.2.1 Introduction 70
3.2.2 Existenceofperiodic(or S-asymptotically) mild or classical solutions 74
3.2.3 Examples 81
3.2.4 Notes and remarks 82
3.3 Square-mean S-asymptoticallyperiodic solutions to fractional stochastic diffusion equations 82
3.3.1 Introduction 82
3.3.2 Existence-uniqueness of square-mean S-asymptotically !-periodic solutions 88
3.3.3 Asymptotically stabilityof square-mean S-asymptotically !-periodic solutions 98
3.3.4 Examples 99
3.3.5 Notes and remarks 100
Chapter4 Existence and Regularityof Solutions toFractional Diffusion Equations 101
4.1 Existence and regularityof solutions to fractional diffusion equations involving time-dependentdiffusion coefficients 101
4.1.1 Introduction 101
4.1.2 Existence and regularityof classical solutions 107
4.1.3 Notes and remarks 118
4.2 Existence and regularityof solutions to fractional diffusion equations involving time-space-dependent diffusion coefficients 118
4.2.1 Introduction 118
4.2.2 Existence and regularityof classical solutions 121
4.2.3 Notes and remarks 128
Bibliography 129
Index 144
编后记 145
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