Fractional Bateman equations in the Atangana-Baleanu sense
Year: 2024
Type: article
Abstract: Considering experimental evidence of fractional behavior for alpha-type radioactive decay, this paper is placed in the context of the fractional Bateman equations with several memory orders. Recent papers studied these equations for Caputo/Riemann-Liouville fractional calculus and suggested the investigation of alternative fractional operators. We focus on the Atangana-Baleanu (AB) formulae, specifically on the associated Volterra integral equations to preserve mass balance. On the one hand, we deal with the associated mathematics of the Bateman model: we solve it in terms of multivariate Mittag-Leffler functions, by means of the Mikusiński operational method, which is more general than the Laplace-transform technique. On the other hand, we address the physical implications of the AB calculus, discussing relevant issues and deficiencies that indicate alternative lines of research.
Source: Physica Scripta
Author: Marc Jornet
Institution: Universitat de València
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,285
OpenAlex ID: W4405623823