In the paper,we implement regular perturbation method (RPM) for 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 the document, the solutions are exact. By comparing these solutions with those obtained by other researchers using other methods for a certain value of the parameter alpha, we obtain the same results.

Linear fractional differential equation, regular perturbation method, Mittag-Leffler, Caputo fractional derivative