An efficient technique for solving fractional diffusion equations arising in oil pollution via natural transform

Abstract

In this paper, we consider the time-fractional non-linear diffusion equations for describing the pollution caused by oil in the water. The hybrid computational technique, the Natural Transform Homotopy Perturbation Technique is applied to get a numerical solution to the time-fractional non-linear diffusion equation. The existence and uniqueness are analyzed with the help of the fixed point theorem, also the stability analysis is discussed by using the Lyapunov function.