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
