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 (IBVPs) for partial differential equations (PDE) with Caputo fractional derivative. According to Bluman's definition and theorem for the symmetry analysis of the PDE system, we determine the symmetries of the PDE with Caputo fractional derivative in general form and prove theorem for the above equation. We investigate the symmetry analysis of IBVP for a fractional diffusion and third-order fractional partial differential equation (FPDE). And as a result of applying the method, we get several solutions.