Discrete Fractional Calculus (2015)

Preface

1. Basic Difference Calculus

1.1. Introduction

1.2. Delta Exponential Function

1.3. Delta Trigonometric Functions

1.4. Second Order Linear Equations with Constant Coefficients

1.5. The Delta Integral

1.6. Discrete Taylor’s Theorem

1.7. First Order Linear Difference Equations

1.8. Second Order Linear Equations (Variable Coefficients)

1.9. Vector Difference Equations

1.10. Stability of Linear Systems

1.11. Floquet Systems

1.12. Exercises

2. Discrete Delta Fractional Calculus and Laplace Transforms

2.1. Introduction

2.2. The Delta Laplace Transform

2.3. Fractional Sums and Differences

2.4. Fractional Power Rules

2.5. Composition Rules

2.6. The Convolution Product

2.7. Using Laplace Transforms to Solve Fractional Equations

2.8. The Laplace Transform of Fractional Operators

2.9. Power Rule and Composition Rule

2.10. The Laplace Transform Method

2.11. Exercises

3. Nabla Fractional Calculus

3.1. Introduction

3.2. Preliminary Definitions

3.3. Nabla Exponential Function

3.4. Nabla Trigonometric Functions

3.5. Second Order Linear Equations with Constant Coefficients

3.6. Chapter

3.7. First Order Linear Difference Equations

3.8. Nabla Taylor’s Theorem

3.9. Fractional Sums and Differences

3.10. Nabla Laplace Transforms

3.11. Fractional Taylor Monomials

3.12. Convolution

3.13. Further Properties of the Nabla Laplace Transform