An efficient technique for solving fractional-order diffusion equations arising in oil pollution

Abstract

In this article, non-linear time-fractional diffusion equations are considered to describe oil pollution in the water. The latest technique, fractional reduced differential transform method (FRDTM), is used to acquire approximate solutions of the time fractional-order diffusion equation and two cases of Allen–Cahn equations. The acquired results are collated with the exact solutions and other results from literature for integer-order $\alpha$, which reveal that the proposed method is effective. Hence, FRDTM can be employed to obtain solutions for different types of nonlinear fractional-order IVPs arising in engineering and science.