Dynamical analysis and numerical treatment of pond pollution model endowed with Caputo fractional derivative using effective wavelets technique

The main objectives of this study are to provide the effective simulation of Pond pollution model under Caputo fractional derivative and to estimate the errors using residual function. For this purpose, a novel Mamadu-Njoseh wavelets have been utilized with approximation approach and collocation nodes to obtain the solutions of fractional Pond pollution model. In few simple steps, the mentioned approach transforms the considered model into a set of easy solvable equations using Chebyshev collocation grids. The accuracy of the numerical results obtained through described approach have been estimated in terms of absolute error and residual error at different wavelets basis. Approximate solutions obtained through the mentioned approach are well comparable with analytical solutions, RK4 method and other techniques. Each computed solutions are presented by tables and graphs to show the impact of the fractional order on the dynamics of pond pollution model. Numerical simulations for the proposed scheme are carried out using software Mathematica, considering different fractional orders. The present investigation demonstrates that the proposed approach is very effective and straightforward for solving such types of fractional models.