Remarks on a green functions approach to diffusion models with singular kernels in fading memories

Abstract

Diffusion problems with singulars kernels in fading memories are very interesting physical problem that have attracted attention of many researchers. In this paper, we aim to provide exact solutions of these problems using the green function method with some integral transform operators. The singular kernel used in this paper is based upon the power law function, which is used to construct the well-known Riemann-Liouville derivative with fractional order.