A numerical approach based on ln-shifted Legendre polynomials for solving a fractional model of pollution

The model of pollution for a system of 3 lakes interconnected by channels is extended using Caputo-Hadamard fractional derivatives of different orders alpha(i) is an element of (0, 1), i = 1, 2, 3. A numerical approach based on ln-shifted Legendre polynomials is proposed to solve the considered fractional model. No discretization is needed in our approach. Some numerical experiments are provided to illustrate the presented method.