Abstract
The fractional model of diffusion equations is very important in the study of oil pollution in the water. The key objective of this article is to analyze a fractional modification of diffusion equations occurring in oil pollution associated with the Katugampola derivative in the Caputo sense. An effective and reliable computational method q-homotopy analysis generalized transform method is suggested to obtain the solutions of fractional order diffusion equations. The results of this research are demonstrated in graphical and tabular descriptions. This study shows that the applied computational technique is very effective, accurate, and beneficial for managing such kind of fractional order nonlinear models occurring in oil pollution.