On the numerical solution for third order fractional partial differential equation by difference scheme method

The exact solution of third order fractional partial differential equations is obtained depending on initial-boundary value problem. The exact solutions and theorem of stability estimates is presented for this equation. Difference schemes are constructed for finite difference scheme. The stability of these difference schemes for this problem are given. Using of these methods, numerical solutions of the third order fractional partial differential equation defined by Caputo fractional derivative for fractional orders ?=0.1, 0.5, 0.9 are calculated. Numerical results are compared with the exact solution and the accuracy and effectiveness of the proposed methods are investigated.