A New Approach to Solve Dynamical Fractional Model of Infertile Couples by The Finite Element Method

In this paper, we propose a dynamic model designed to predict the treatment outcomes of infertility in couples. To this end, five main groups of couples are considered: susceptible couples, patient couples, those undergoing treatment only, those receiving treatment with surgery, and cured couples. Our primary contribution lies in the formulation of a fractional-order model that captures the dynamics of infertile couples and identifies asymptotically stable disease-free equilibrium points. The main objective is to develop a novel numerical approach based on the finite element method to solve a nonlinear system of fractional differential equations. This method transforms the fractional system into a system of algebraic equations. Moreover, the proposed technique proves to be robust, efficient, and particularly well-suited to modeling infertility. To validate our model, we apply the proposed method and conclude with a comprehensive numerical analysis.