A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation

Abstract

In this paper, an optimization method based on the generalized polynomials (GPs) as the basis functions is proposed for solving the variable-order time fractional Burgers’ equation (V-TFBE). In this method, the solution is considered as an GPs with unknown free coefficients and control parameters. The primary purpose of this paper is to employ a new variable-order operational matrix for GPs in the Caputo sense. Then we use the Lagrange multipliers technique for converting the problem under study into a system of nonlinear algebraic equations with unknown free coefficients and control parameters which constructs an approximate solution for the problem under study. The convergence analysis is guaranteed by obtaining a new result concerning the functions of two variables. The efficiency of the proposed method is illustrated by three numerical experiments, which confirm that obtained results are in good agreement with the exact solution.