The Solutions of the Linear Fractional Diffusion and Diffusion-convection Equations via the Regular Perturbation Method (RPM)

In this paper, we implement Regular Perturbation Method (RPM) for the Solving fractional diffusion and diffusion-convection equations, in order to determine the analytical solutions of some linear fractional diffusion and linear fractional diffusion-convection equations. In general, the solving using this method allow to obtain exact or approximate solutions. For the case of the diffusion and diffusion-convection equations solved in this document, the solutions obtained are exact. By comparing these solutions with those obtained by other researchers using other methods for a certain value of the parameter α, we obtain the same results.