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

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