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- 2018
Non-Gaussian Distributions to Random Walk in the Context of Memory KernelsDOI: https://doi.org/10.3390/fractalfract2030020 Keywords: fractional diffusion equation, memory kernels, random walk, diffusion models, solution techniques, anomalous diffusion Abstract: Abstract 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. View Full-Tex
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