A novel wavelets operational matrix method for the time variable-order fractional mobile–immobile advection–dispersion model

Abstract

A novel computational technique for the solution of the variable-order fractional mobile–immobile advection–dispersion equation has been presented in this paper. Firstly, operational integration matrices and variable-order fractional derivatives were deduced using Boubaker wavelets to implement this proposed technique. Utilizing Boubaker wavelets basis for functions approximations and the operational matrices of integration and variable-order fractional derivative along with collocation points, the variable-order fractional mobile–immobile advection–dispersion equation is reduced into the system of algebraic equations. In addition, to determine the convergence analysis and error estimate of the proposed numerical technique, some useful theorems are discussed. Finally, to analyze the computational efficiency and applicability of the proposed numerical method, several numerical examples are presented.