An efficient numerical approach for solving fractional model of nonautonomous seasonal eco-epidemic system by using Bernoulli wavelets

In this study, the Bernoulli wavelet method is employed to solve a nonlinear fractional seasonal eco-epidemic model. This paper introduces an operational matrix using Bernoulli wavelets to solve a system of nonautonomous fractional differential equations involving time-dependent disease transmission rates between predator and preys, mortality rate of sick predators, predation rate on healthy preys, and an extra food supply. This approach involves transforming the differential equation system into a system of algebraic equations, simplifying the solution process. We analyzed the convergence and stability analysis of the proposed iterative method. We have also examined the solution of aforementioned differential equations system using the Toufik–Atangana scheme to assess the accuracy and suitability of the Bernoulli wavelet approach. Additionally, several numerical simulations have been conducted to validate our findings.