An innovative q-homotopy analysis approach for solving generalized q-fractional non-linear biological population model

This paper presents an innovative approach for solving the generalized q-fractional non-linear biological population model through synthesis of a semi-analytical technique called the q-homotopy analysis method (qHAM). The qHAM is extended to merge q-fractional Laplace transform to obtain approximations in both non-linear and linear terms of q-fractional partial differential equations (q-FPDEs). The q-FPDEs are important types of fractional q-equations in q-calculus that have recently captured the attention of researchers due to their importance in engineering applications, especially in quantum mechanics. The biological population model is used to describe the dynamics of population changes over time, and growth of viruses, parasites, and illnesses may also be explained using this model. A biological population model may manage the devolution of delicate species by treading carefully on them. Duo to the model’s importance, we find an approximate solution with high accuracy, and to confirm this, we compare our results with the solutions in other approaches. We study the convergence of the solutions obtained. The results have also been elucidated by presenting the solutions in two- and three-dimensional graphs to show the influence of different parameters on the system.