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 an earks
2.2 Initial problems for fractional diffusion equations in fractionalpower spaces
I2.2.1 ntroduction
2.2.2 Existence of q-mild solutions 25
2.. Existence of q-classical solutions 30
2.2.4 Applications 30
2.2.5 Notes an earks 32
. Positive mild solutionstoperiodicboundaryvalue problemsfor fractional diffusion equations 32 Introduction 32
..1 Contents
..2 Existence of mild solutions 38
.. Examples 40
..4 Notes an earks 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 an earks 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 an earks 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.. Examples 81
3.2.4 Notes an earks 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 an earks 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 an earks 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.. Notes an earks 128
Bibliography 129
Index 144
编后记 145
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