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

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 numerical solution of fractional-order Kolmogorov and Rosenau–Hyman models. Fractional-order models are widely used in physics, engineering, other fields. However, their solutions difficult obtain due non-linearity non-locality overcomes these challenges by transforming equations into series linear that can be solved numerically. results show an effective accurate models, it study wide range phenomena various