分数阶时滞微分方程的研究PDF电子书下载

Chapter 1 Introduction 1

1.1 Fractional Calculus 1

1.2 Outline of This Book 5

Chapter 2 Overview of Solutions to Fractional ODEs 9

2.1 Existence Results of Fractional ODEs on a Finite Interval of the Real Axis 9

2.2 Global Solutions to ODEs with the Riemann-Liouville Derivative 17

2.3 Local Solutions to ODEs with the Riemann-Liouville Derivative 19

2.4 The Cauchy Problems of ODEs with the Caputo Derivative 22

Chapter 3 Existence of Nonlinear FFDEs 27

3.1 Problem Formulation 27

3.2 Definitions and Lemmas 29

3.3 Existence Results of Fractional-Order FDEs 30

3.4 An Illustrative Example 38

Chapter 4 Solutions of Linear Fractional Delayed Differential Equations 40

4.1 On the Solution of Fractional Delayed Differential Systems 40

4.2 General Solution of Linear Fractional Neutral DDEs 45

4.3 Variation of Constant Formulae for Fractional DDEs 55

Chapter 5 Stability of Fractional Delayed Differential Equations 68

5.1 Stability of Fractional Linear Singular Delayed Differential Systems 68

5.2 Stability of Fractional Neutral Dynamical Systems with Multiple Delays 83

5.3 Finite-Time Stability of Fractional Distributed Delayed Neural Networks 99

Chapter 6 Controllability of Fractional Delayed Differential Systems 107

6.1 Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses 108

6.2 Reachability and Controllability of Fractional Singular Dynamical Systems with Control Delay 121

References 140