Symmetry Analysis of Initial and Boundary Value Problems for Fractional Differential Equations in Caputo sense

In this work we study Lie symmetry analysis of initial and boundary value problems for partial differential equations (PDE) with Caputo fractional derivative. We give generalized definition and theorem for the symmetry method for PDE with Caputo fractional derivative, according to Bluman's definition and theorem for the symmetry analysis of PDE system. We investigate the symmetry analysis of initial and boundary value problem for fractional diffusion and the third order fractional partial differential equation (FPDE). Also we give some solutions.