Some Finite Difference Methods for Solving Fractional Differential Equations

The main purpose of this work is to study the numerical solutions for special types of the fractional differential equations via the finite difference methods with their stability. This study includes the following aspects:

1. Give some definitions of the fractional order ordinary derivatives with their generalization for the partial ones.
2. Study the existence of the solutions and extermal solutions for special types of the fractional order ordinary differential equations.
3. Use the explicit and the implicit finite difference methods with a study of their stability to solve special types of the one-sided and two-sided fractional order ordinary and partial differential equations.