A novel high-order explicit exponential integrator scheme for the space–time fractional Bloch–Torrey equation

In this paper, the space–time fractional Bloch–Torrey equation is discretized in space using second and fourth-order schemes. Then, it leads to a system of Caputo fractional ordinary differential equations over time. A highly accurate exponential integrator is utilized to solve systems of fractional differential equations. We rigorously demonstrate the stability and convergence of the schemes by employing the energy technique. Finally, some numerical examples are presented to validate the accuracy and efficiency of the proposed algorithms.