Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels

Fractal and Fractional

Dos Santos, Maike A. F.¹ 

[1] Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil

关键词: fractional diffusion equation;    memory kernels;    r;    om walk;    diffusion models;    solution techniques;    anomalous diffusion;   

DOI  :  10.3390/fractalfract2030020

学科分类：数值分析

来源: mdpi

【 摘 要 】

The investigation of diffusive process in nature presents a complexity associated with memory effects. Thereby, it is necessary new mathematical models to involve memory concept in diffusion. In the following, I approach the continuous time random walks in the context of generalised diffusion equations. To do this, I investigate the diffusion equation with exponential and Mittag-Leffler memory-kernels in the context of Caputo-Fabrizio and Atangana-Baleanu fractional operators on Caputo sense. Thus, exact expressions for the probability distributions are obtained, in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class of diffusive behaviour. Moreover, I propose a generalised model to describe the random walk process with resetting on memory kernel context.

【 授权许可】

CC BY