Reproducing kernel functions-based meshless method for variable order fractional advection-diffusion-reaction equations

Abstract

In this paper, on the basis of the reproducing kernel functions, a novel meshless algorithm is explored for fractional advection–diffusion-reaction equations (ADREs) with Caputo time variable order. Firstly, the Gaussian kernel function and the Mittag–Leffler kernel function are introduced and combined to construct a new binary reproducing kernel function. Secondly, base on the constructed reproducing kernel function, by employing the space–time collocation technique, a novel meshless method is proposed for fractional ADREs. Numerical experiments are implemented and the numerical results show the potential of our new approach for fractional ADREs.