{"title":"用米库辛斯基代数微积分分析放射性衰变中的多期分数贝特曼方程","authors":"Marc Jornet","doi":"10.1016/j.cjph.2024.10.002","DOIUrl":null,"url":null,"abstract":"<div><div>Fractional Bateman equations model the concentrations of nuclear species through a radioactive decay chain, by considering non-Markovian behavior. Cruz-López and Espinosa-Paredes (Nuclear Engineering and Technology, 2022) solved the mathematical problem with a single memory coefficient, based on the Laplace-transform technique. Cruz-López, Espinosa-Paredes and François (Computer Physics Communications, 2022) extended the analysis to several fractional orders, with Laplace transforms and series expansions checked by induction. In this paper, we solve such a case of distinct memory effects, via the more general method of Mikusiński operational calculus. We do not distinguish between equal and different decay rates. Multivariate Mittag-Leffler functions appear in the closed-form expression.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"92 ","pages":"Pages 623-630"},"PeriodicalIF":4.6000,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of the multi-term fractional Bateman equations in radioactive decay by means of Mikusiński algebraic calculus\",\"authors\":\"Marc Jornet\",\"doi\":\"10.1016/j.cjph.2024.10.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Fractional Bateman equations model the concentrations of nuclear species through a radioactive decay chain, by considering non-Markovian behavior. Cruz-López and Espinosa-Paredes (Nuclear Engineering and Technology, 2022) solved the mathematical problem with a single memory coefficient, based on the Laplace-transform technique. Cruz-López, Espinosa-Paredes and François (Computer Physics Communications, 2022) extended the analysis to several fractional orders, with Laplace transforms and series expansions checked by induction. In this paper, we solve such a case of distinct memory effects, via the more general method of Mikusiński operational calculus. We do not distinguish between equal and different decay rates. Multivariate Mittag-Leffler functions appear in the closed-form expression.</div></div>\",\"PeriodicalId\":10340,\"journal\":{\"name\":\"Chinese Journal of Physics\",\"volume\":\"92 \",\"pages\":\"Pages 623-630\"},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chinese Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0577907324003927\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chinese Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0577907324003927","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Analysis of the multi-term fractional Bateman equations in radioactive decay by means of Mikusiński algebraic calculus
Fractional Bateman equations model the concentrations of nuclear species through a radioactive decay chain, by considering non-Markovian behavior. Cruz-López and Espinosa-Paredes (Nuclear Engineering and Technology, 2022) solved the mathematical problem with a single memory coefficient, based on the Laplace-transform technique. Cruz-López, Espinosa-Paredes and François (Computer Physics Communications, 2022) extended the analysis to several fractional orders, with Laplace transforms and series expansions checked by induction. In this paper, we solve such a case of distinct memory effects, via the more general method of Mikusiński operational calculus. We do not distinguish between equal and different decay rates. Multivariate Mittag-Leffler functions appear in the closed-form expression.
期刊介绍:
The Chinese Journal of Physics publishes important advances in various branches in physics, including statistical and biophysical physics, condensed matter physics, atomic/molecular physics, optics, particle physics and nuclear physics.
The editors welcome manuscripts on:
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Plasma and Beam Physics-
Condensed Matter: Structure, etc.-
Condensed Matter: Electronic Properties, etc.-
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CJP publishes regular research papers, feature articles and review papers.