Different Approaches for Solving Fractional Differential Equations

Abstract

1. Introduction, we present a brief history of fractional operators and we explain the importance of Sinc method then introduce our aim of thesis.

2. In chapter 1, we present the basics needed in thesis and it contains the most important definitions, examples and theorems, where we explain some basics of Sinc function, conformal map, Sinc basis, Sinc approximation and singular points.

3. In chapter 2, we make a survey on some numerical methods which used to solve the differential equations, these methods are under the titles fi-nite element methods, Spectral methods, finite difference methods and Sinc method and we state some properties of Sinc function with proofs, and in-troduce different definitions of fractional operators introduced by Riemann

- Liouville and Caputo, then state fractional differential equations, and we explain how to convert them to convolution integrals by the definition of Riemann - Liouville, also we discuss Sinc method to solve indefinite and convolution integrals and then review the solution of fractional differential equations.

4. In chapter 3, we solve some applications of fractional differential equations with a fractional operator and with several fractional operators by using Sinc method and compare our results with the pervious results from other methods, also we use Thieles algorithm for approximation. The new result is already accepted for publication under title