A meshless method based on the modified moving Kriging interpolation for numerical solution of space-fractional diffusion equation

Fractional differential equations (FDEs) offer numerous capabilities for modeling unusual phenomena. So, the study of these models is essential. This paper proposes an efficient meshless technique for obtaining the numerical solution of a space fractional diffusion model with Caputo derivative type. Typically, in a meshless processes based on moving Kriging (MK) interpolation, the MK technique is used to calculate the shape functions and their derivatives with positive integer order against space variables to discretize the governing equation in space variables. However, in this study, we employ the Taylor series of MK interpolation's correlation function to enhance the shape function derivatives for arbitrary order 0.5 < alpha < 2. Moreover, the finite difference technique is employed to discretize the model in the time dimension and its characterized by unconditional stability and a rate of convergence of O(tau). This approach converts the primary problem into a system of linear algebraic equations. Finally, we present several examples in one and two dimensions and compare the results with other well-known schemes to show the capability and accuracy of this approach.