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 α_i∈(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.