Application of the q-Homotopy Analysis Transform Method to Fractional-Order Kolmogorov and Rosenau–Hyman Models within the Atangana–Baleanu Operator

Abstract

The q-homotopy analysis transform method (q-HATM) is a powerful tool for solving differential equations. In this study, we apply the q-HATM to compute the numerical solution of the fractional-order Kolmogorov and Rosenau–Hyman models. Fractional-order models are widely used in physics, engineering, and other fields. However, their numerical solutions are difficult to obtain due to the non-linearity and non-locality of the equations. The q-HATM overcomes these challenges by transforming the equations into a series of linear equations that can be solved numerically. The results show that the q-HATM is an effective and accurate method for solving fractional-order models, and it can be used to study a wide range of phenomena in various fields.