The solution of differantial equations with fractional order solutions by using finite difference methods and Adomian decomposition methods

This study constructed six chapters. In chapter one, it has been given informations about using areas and historical structure. In chapter two, some fundamental definitions have been given. In chapter three, fractional integration and derivative definitions in terms of different aspects have been given. In chapter four, the fundamental structures of Finite Differance Method and Adomian Decomposition Method have been given. And also the calculation Adomian polinoms which arise during applying Adomian Decomposition Method has given. In chapter five, Finite Difference Method and Adomian Decomposition Method have been applied to the fractional diffusion equation along with initial and boundary conditions. Investigations of obtained solutions by using Finite Difference Method and Adomian Decomposition Method, 3D graphics, tables and numerical data errors for every of techniques have been maden. In chapter six, informations about suitability of Finite Difference Method and Adomian Decomposition Method for fractional diffusion equations have been given.