Fractional derivative with non-singular kernels in anomalous relaxation and diffusion modeling

HongGuang Sun, Xiaoxiao Hao, Yong Zhang, Dumitru Baleanu

Published 2016-06-11Version 1

Anomalous relaxation and diffusion processes are major application area of fractional derivative models. This paper offers an investigation on physical behavior of fractional derivative relaxation and diffusion models by using a new definition of fractional derivative with exponential kernel. Our analytical results indicate that the fractional derivative models with new definition cannot well characterize non-exponential nature of anomalous relaxation and diffusion processes. Hereby, this paper introduces a legitimate extension of fractional derivative by replacing exponential kernel with a stretched exponential kernel. Numerical results illustrate the fractional derivative model with stretched exponential kernel can describe wide range of anomalous physical phenomena, compared with the exponential kernel.