Solving fractional diffusion equations by Sinc and radial basis functions

Abstract

In this study, we approximate the solution of the fractional diffusion equations based on Gaussian radial basis function (GRBF). Our approach is based on the Caputo fractional derivative and the combination of GRBF and Sinc function, here the GRBF direct and GRBF-QR methods are developed. The Sinc quadrature rule combined with double exponential transformation (DE) has been used to approximate the fractional integral. Three examples have been considered to test the presented methods, we compared the results to verify the effectiveness of the presented methods against recent existing methods diven by [A radial basis functions method for fractional diffusion equations, J. Comput. Phys. 238 (2013) 71–81; An efficient Chebyshev-tau method for solving the space fractional diffusion equations, Appl. Math. Comput. 224 (2013) 259–267; A tau approach for solution of the space fractional diffusion equations, Comput. Math. Appl. 62 (2011) 1135–1142], and also conclude that GRBF-QR-Sinc method demonstrates better accuracy.