Mittag–Leffler Memory Kernel in Lévy Flights

Clicks: 191
ID: 33199
2019
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Abstract
In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag−Leffler kernel in the context of Atangana−Baleanu operator. The Lévy process has several applications in science, with a particular emphasis on statistical physics and biological systems. Using the continuous time random walk, we constructed a fractional diffusion equation that includes two fractional operators, the Riesz operator to Laplacian term and the Atangana−Baleanu in time derivative, i.e., a A B D t α ρ ( x , t ) = K α , μ ∂ x μ ρ ( x , t ) . We present the exact solution to model and discuss how the Mittag−Leffler kernel brings a new point of view to Lévy process. Moreover, we discuss a series of scenarios where the present model can be useful in the description of real systems.
Reference Key
santos2019mittaglefflermathematics Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Santos, Maike A. F. dos;
Journal Mathematics
Year 2019
DOI
DOI not found
URL
https://www.mdpi.com/2227-7390/7/9/766
Keywords Keywords not found

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