Anomalous Diffusion Models With General Fractional Derivatives Within the Kernels of the Extended Mittag-Leffler Type Functions

Abstract

This paper addresses the new general fractional derivatives (GFDs) involving the kernels of the extended Mittag-Leffler type functions (MLFs). With the aid of the GFDs in the MLF kernels, the mathematical models for the anomalous diffusion of fractional order are analyzed and discussed. The proposed formulations are also used to describe complex phenomena that occur in heat transfer.