Non-Gaussian distributions to random walk in the context of memory kernels

• Autor(a) principal: Santos, Maike Antonio Faustino dos
• Data de Publicação: 2018
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRGS
• Texto Completo: http://hdl.handle.net/10183/195080
• topic: Física estatística; Probabilidade; Processos estocásticos; Fractional diffusion equation; Memory kernels; Random walk; Diffusion models; Solution techniques; Anomalous diffusion

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.