The Solution of Fractional Diffusion-reaction Equation Via the Regular Perturbation Method (RPM)
Bationo Jérémie Yiyuréboula *
University Joseph Ki Zerbo, Burkina Faso.
Yaya Moussa
University Joseph Ki Zerbo, Burkina Faso.
Bassono Francis
University Joseph Ki Zerbo, Burkina Faso.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we implement Regular Perturbation Method (RPM) of the Solving fractional diffusion-reaction equation, in order to determine the exact analytical solutions of some linear fractional diffusion-reaction equation. 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 \(\alpha\), we obtain the same results.
Keywords: Linear fractional diferential equation, regular perturbation method, Mittag-Leer, Caputo fractional derivative or integral