Abstract
The present paper deals with the numerical solution of space–time-fractional reaction–diffusion problems used to model some complex phenomena that are governed by dynamic of anomalous diffusion. The time- and space-fractional reaction–diffusion equation is modeled by replacing the first-order derivative in time and the second-order derivative in space, respectively, with the Caputo and Riesz operators. We propose an adaptable numerical scheme for the approximation of the derivatives. Accuracy of the method is justified by reporting both the maximum error and relative error in 2D with analytical solutions given. The effectiveness and applicability of the proposed methods are tested on two of practical problems that are of current and recurring interests in one and two dimensions to cover pitfalls that may arise.
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