A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations

This paper addresses a stable three -level explicit scheme for a class of nonlinear time variable order fractional partial differential equations. The proposed strategy is based on the linear B-spline approximation of the time variable order fractional derivative in the Caputo sense and the Du Fort-Frankel algorithm. The unconditional stability and the convergence of the scheme are established. Several numerical results confirm the accuracy and efficiency of the novel scheme. (C) 2016 Elsevier Ltd. All rights reserved.