Numerical study of multidimensional fractional time and space coupled Burgers’ equations

Abstract

This paper declares a new spectral collocation technique to provide accurate approximate solutions of the one- and two-dimensional time and space fractional coupled Burgers’ equations (TSFCBEs) in which the fractional derivatives are defined according to Caputo’s definition. The suggested method is based on the shifted Gegenbauer polynomials (SGPs) for approximating the solution of TSFCBEs. The suggested technique reduces the considered problems to the solution of nonlinear algebraic equations (NLAEs). Moreover, the accuracy and reliability of the proposed method are confirmed through numerical examples. Finally, the obtained numerical results are compared with those previously reported in the literature.