A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation

Abstract In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is employed to define a new fractional version of 2D reaction-advection-diffusion equation. An efficient and accurate hybrid method based on the shifted orthogonal Bernoulli polynomials and radial basis functions is developed for solving this equation. The presented method converts solving the problem under consideration into solving a system of algebraic equations. The applicability and accuracy of the proposed method are investigated by solving some numerical examples.