A second-order numerical scheme for the time-fractional partial differential equations with a time delay

This work proposes a numerical scheme for a class of time-fractional convection–reaction–diffusion problems with a time lag. Time-fractional derivative is considered in the Caputo sense. The numerical scheme comprises the discretization technique given by Crank and Nicolson in the temporal direction and the spline functions with a tension factor are used in the spatial direction. Through the von Neumann stability analysis, the scheme is shown conditionally stable. Moreover, a rigorous convergence analysis is presented through the Fourier series. Two test problems are solved numerically to verify the effectiveness of the proposed numerical scheme.