An optimization method based on the generalized Lucas polynomials for variable-order space-time fractional mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels

Abstract

Abstract This paper introduces a novel version of variable-order (VO) space-time mobile-immobile advection-dispersion equation involving derivatives with non-singular kernels. An optimization scheme is proposed for solving this new class of VO fractional problems.The presented method is based on the hybrid of the generalized Lucas polynomials together with their operational matrices of VO fractional derivatives (which are obtained for the first time in the presented study), the collocation technique and the Lagrange multipliers scheme. The presented method transforms obtaining the solution of such problems into obtaining the solution of systems of algebraic equations. Two numerical examples are provided to show the validity and accuracy of the presented approach.