ABSTRACT
In this chapter, a new approximate solution for the fractional diffusion equation described by the Caputo-generalized fractional derivative has been presented. The heat balance integral method and the double integral method have been used for getting an approximate solution of the generalized fractional diffusion equation. The effect of the order $\rho$ in the diffusion process has been analyzed. The approximate solution of the fractional diffusion equation described by the integer-order derivative, the approximate solution of the fractional diffusion equation represented by the Caputo derivative and the approximate solution of the fractional diffusion equation expressed by the Caputo-generalized fractional derivative have been proposed and compared.
