Discrete Fractional Calculus (2015)
1. Basic Difference Calculus
1.2. Delta Exponential Function
1.3. Delta Trigonometric Functions
1.4. Second Order Linear Equations with Constant Coefficients
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
2. Discrete Delta Fractional Calculus and Laplace Transforms
2.2. The Delta Laplace Transform
2.3. Fractional Sums and Differences
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
3. Nabla Fractional Calculus
3.3. Nabla Exponential Function
3.4. Nabla Trigonometric Functions
3.5. Second Order Linear Equations with Constant Coefficients
3.7. First Order Linear Difference Equations
3.9. Fractional Sums and Differences
3.10. Nabla Laplace Transforms