Exactly explicit solutions of (2+1)-dimensional conformable fractional diffusive Predator–Prey model via neural networks method

In this paper, a solver is developed to obtain accurate analytical solutions for fractional partial differential equations based on artificial neural networks. By leveraging the powerful function approximation capability of neural networks in combination with the trial function method, a general analytical solution approach for fractional partial differential equations is proposed. The method is applied to a (2 + 1)-dimensional conformable fractional diffusive predator–prey system, and a series of exact analytical solutions are successfully derived. With the aid of Python mathematical software, three-dimensional surface plots, two-dimensional curve plots, gradient field plots, and contour plots in polar coordinates for selected solutions are generated to visually illustrate the morphological characteristics of the solutions. These implementations collectively verify the effectiveness and practicality of the proposed method.