 On the random fractional Bateman equationsMarc Jornet Applied Mathematics and Computation, 2023, vol. 457, issue C Abstract: We study the random fractional Bateman equations for a radioactive decay chain, in the Caputo-derivative sense. On the one hand, a fractional order entails memory effects in the system, and on the other hand, randomness accounts for uncertainties on the physical quantities. Results on the deterministic fractional Bateman equations and on the random ordinary Bateman equations were recently published. The proposed stochastic fractional model extends these previous works. We construct the stochastic solution; first, in the pathwise sense by using the Laplace-transform method, and second, in the mean-square sense by applying Banach fixed-point theorem. The probability density function, that is associated to the solution of a chain of length three, is computed in the present work by a transformation method. Continuity of this density with respect to the fractional order, in the pointwise and in the total variation sense, is investigated. Numerical results are included for forward uncertainty quantification, with the purpose of illustrating the developed theory. Keywords: Radioactive decay chain model; Random fractional differential-algebraic equation; Mean-square calculus; Probability density function; Uncertainty quantification (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003661 DOI: 10.1016/j.amc.2023.128197 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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