An RBF based meshless method for the distributed order time fractional advection-diffusion equation

Distributed order operators and differential equations have been applied to model physical phenomena. Then the numerical methods for these problems are required. In this paper, we consider a meshless method for solving a distributed order time fractional advection-diffusion equation. After discretizing the outer integral in the distributed order derivative and the first derivative in the interior integral of the Caputo fractional derivative using the trapezoid formula and the first order difference approximation, respectively, a semi-discrete scheme is obtained. Then for every fixed time, approximating the solution using radial basis function (RBF), a fully discrete scheme is obtained. Five numerical examples in bounded domains containing irregularly shaped domains are presented to show the application of the present technique.