Fractal and Fractional | |
Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels | |
Dos Santos, Maike A. F.1  | |
[1] Instituto de FÃsica, 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
【 预 览 】
Files | Size | Format | View |
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RO201910254019603ZK.pdf | 965KB | download |