A Composite collocation method based on the fractional Chelyshkov wavelets for Distributed-order fractional Mobile-immobile advection-dispersion equation

In this study, an accurate and efficient composite collocation method based on the fractional order Chelyshkov wavelets is proposed for obtaining approximate solution of distributed-order fractional mobile-immobile advection-dispersion equation with initial and boundary conditions. Operational matrices based on the fractional Chelyshkov wavelets are constructed. The proposed method reduce the solution to a system of algebraic equations, which is solved by Newton’s iterative method. Provided examples confirm the accuracy and applicability of the proposed method in line with the studied convergence analysis and error estimation. The obtained results of demonstrated numerical schemes illustrate that this approach is very accurate and efficient.