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.