Intro
Preface
Contents
1 Introduction
1.1 Brief History
1.2 Special Functions
1.3 Laplace Transform
1.4 Inverse Laplace Transform
1.5 Fixed Point Theorems
1.6 Function Spaces
1.7 Exercises
References
2 Fractional Calculus
2.1 Preliminaries
2.2 Riemann-Liouville Fractional Integrals and Derivatives
2.3 Caputo Fractional Derivatives
2.4 Examples
2.5 Exercises
References
3 Fractional Differential Equations
3.1 Motivation
3.2 Equation with Constant Coefficient
3.3 Equation with Matrix Coefficient
3.4 Nonlinear Equations

3.5 Nonlinear Damped Equations
3.6 Examples
3.7 Exercises
References
4 Applications
4.1 Observability
4.2 Controllability of Linear Systems
4.3 Controllability of Nonlinear Systems
4.4 Stability
4.5 Nonlinear Equations
4.6 Examples
4.7 Exercises
References
5 Fractional Partial Differential Equations
5.1 Motivation
5.2 Fractional Partial Integral and Derivative
5.3 Linear Fractional Equations
5.3.1 Adomian Decomposition Method
5.3.2 Fractional Diffusion Equation
5.3.3 Fractional Wave Equation
5.3.4 Fractional Black-Scholes Equation

5.4 Nonlinear Fractional Equations
5.4.1 Dirichlet Boundary Condition
5.4.2 Neumann Boundary Condition
5.5 Fractional Equations with Kernel
5.6 Examples
5.7 Exercises
References
6 Fractional Integrals and Derivatives
6.1 Definitions of Fractional Integrals
6.2 Definitions of Fractional Derivatives
6.3 Comments
6.4 Examples
6.5 Exercises
References
Appendix Index
Index