Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations

In this paper, we develop a range of efficient and fast fractional difference schemes for the approximation of Caputo time-fractional subdiffusion-reaction equations. The classical time derivative is replaced with the Caputo fractional derivative operator. The experimental results justify that the numerical solution of the proposed methods compares favourably with the exact solution. Experimental results give a clear indication that dynamical models with non-integer order can yield a better spatial pattern when compared with their classical counterparts.