Numerical approximation of space-fractional diffusion equation using Laguerre spectral collocation method

The space-fractional diffusion equation is extensively used to model various issues in engineering and mathematics. This paper addresses the numerical approximation of the space-fractional-order diffusion equation, using a fractional operator in the Caputo sense. The proposed equation is computed numerically through the Laguerre spectral collocation method combined with the finite difference scheme. The results were visualized using MATLAB R2016a, and the accuracy of the numerical scheme was validated by comparing the approximate results with those derived from exact values and the Legendre spectral collocation technique. The originality of this study lies in the application of the Laguerre spectral collocation method for fractional-order diffusion equations in the Caputo sense. Two numerical problems were included to demonstrate the validity and applicability of the proposed technique. The obtained results confirm that this method aligns well with the exact values and the Legendre spectral collocation method, as shown in tabular and graphical simulations.