{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T06:03:14Z","timestamp":1780293794555,"version":"3.54.0"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T00:00:00Z","timestamp":1768521600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T00:00:00Z","timestamp":1768521600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s40314-025-03594-0","type":"journal-article","created":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T08:24:44Z","timestamp":1768551884000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Constructing mean square series solutions for a class of one-dimensional linear fractional random differential equations via the Laplace transform"],"prefix":"10.1007","volume":"45","author":[{"given":"L.","family":"Villafuerte","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Trevi\u00f1o","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,16]]},"reference":[{"key":"3594_CR1","first-page":"52","volume":"1","author":"A Akg\u00fcl","year":"2020","unstructured":"Akg\u00fcl A, Khoshnaw S (2020) Application of fractional derivative on non-linear biochemical reaction models. Int J Intell Netw 1:52\u201358","journal-title":"Int J Intell Netw"},{"key":"3594_CR2","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/j.cnsns.2018.04.019","volume":"64","author":"H Sun","year":"2018","unstructured":"Sun H, Zhang Y, Baleanu D, Chen W, Chen Y (2018) A new collection of real world applications of fractional calculus in science and engineering. Commun Nonlinear Sci Numer Simul 64:213\u2013231","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"2","key":"3594_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2021.125412","volume":"504","author":"P Wu","year":"2021","unstructured":"Wu P, Yang Z, Wang H, Song R (2021) Time fractional stochastic differential equations driven by pure jump L\u00e9vy noise. J Math Anal Appl 504(2):125412","journal-title":"J Math Anal Appl"},{"key":"3594_CR4","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1007\/s00780-019-00400-8","volume":"23","author":"CD Constantinescu","year":"2019","unstructured":"Constantinescu CD, Ramirez JM, Zhu WR (2019) An application of fractional differential equations to risk theory. Finance Stochast 23:1001\u20131024","journal-title":"Finance Stochast"},{"key":"3594_CR5","first-page":"135","volume":"7","author":"AMA El-Sayed","year":"2017","unstructured":"El-Sayed AMA, Gaafar F (2017) El-Gendy: Continuous dependence of the solution of random fractional-order differential equation with nonlocal conditions. Fract Calc Appl Anal 7:135\u2013149","journal-title":"Fract Calc Appl Anal"},{"issue":"2","key":"3594_CR6","first-page":"119","volume":"4","author":"V Lupulescu","year":"2012","unstructured":"Lupulescu V, Ntouyas SK (2012) Random fractional differential equations. Int Electron J Pure Appl Math 4(2):119\u2013126","journal-title":"Int Electron J Pure Appl Math"},{"key":"3594_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.93.180603","volume":"93","author":"SC Kou","year":"2004","unstructured":"Kou SC, Xie XS (2004) Generalized langevin equation with fractional gaussian noise: Subdiffusion within a single protein molecule. Phys Rev Lett 93:180603","journal-title":"Phys Rev Lett"},{"key":"3594_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2023.107202","volume":"121","author":"H Vu","year":"2023","unstructured":"Vu H, Phu ND, Hoa NV (2023) A survey on random fractional differential equations involving the generalized caputo fractional-order derivative. Commun Nonlinear Sci Numer Simul 121:107202","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"3594_CR9","doi-asserted-by":"publisher","first-page":"9037","DOI":"10.1002\/mma.4881","volume":"41","author":"C Burgos","year":"2018","unstructured":"Burgos C, Calatayud J, Cort\u00e9s J-C, Navarro-Quiles A (2018) A full probabilistic solution of the random linear fractional differential equation via the random variable transformation technique. Math Method Appl Sci 41:9037\u20139047","journal-title":"Math Method Appl Sci"},{"key":"3594_CR10","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.aml.2017.11.009","volume":"78","author":"C Burgos","year":"2018","unstructured":"Burgos C, Calatayud J, Cort\u00e9s J-C, Villafuerte L (2018) Solving a class of random non-autonomous linear fractional differential equations by means of a generalized mean square convergent power series. Appl Math Lett 78:95\u2013104. https:\/\/doi.org\/10.1016\/j.aml.2017.11.009","journal-title":"Appl Math Lett"},{"key":"3594_CR11","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1016\/j.chaos.2017.02.008","volume":"102","author":"C Burgos","year":"2017","unstructured":"Burgos C, Cort\u00e9s J-C, Villafuerte L, Villanueva R-J (2017) Extending the deterministic riemann-liouville and caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations. Chaos Solit Fract 102:305\u2013318","journal-title":"Chaos Solit Fract"},{"key":"3594_CR12","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.cam.2017.12.042","volume":"339","author":"C Burgos","year":"2018","unstructured":"Burgos C, Cort\u00e9s J-C, Villafuerte L, Villanueva RJ (2018) Solving random mean square fractional linear differential equations by generalized power series: Analysis and computing. J Comput Appl Math 339:94\u2013110","journal-title":"J Comput Appl Math"},{"key":"3594_CR13","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.matcom.2023.03.001","volume":"210","author":"L Villafuerte","year":"2023","unstructured":"Villafuerte L (2023) Solution processes for second-order linear fractional differential equations with random inhomogeneous parts. Math Comput Simul 210:17\u201348","journal-title":"Math Comput Simul"},{"issue":"16","key":"3594_CR14","doi-asserted-by":"publisher","first-page":"4846","DOI":"10.1002\/mma.3818","volume":"39","author":"R Almeida","year":"2015","unstructured":"Almeida, R., Monteiro, M.T., Nuno, B. (2015) Modeling some real phenomena by fractional differential equations. Mathematical Methods in the Applied Sciences. (39)16: 4846\u20134855","journal-title":"Math Methods Appl Sci"},{"key":"3594_CR15","volume-title":"Random Differential Equations in Science and Engineering","author":"TT Soong","year":"1973","unstructured":"Soong TT (1973) Random Differential Equations in Science and Engineering. Academic Press, New York"},{"key":"3594_CR16","first-page":"1","volume":"418","author":"C Burgos","year":"2022","unstructured":"Burgos C, Cort\u00e9s JC, Villafuerte L, Villanueva RJ (2022) Solving random fractional second-order linear equations via the mean square Laplace transform: Theory and statistical computing. Appl Math Comput 418:1\u201317","journal-title":"Appl Math Comput"},{"key":"3594_CR17","first-page":"1209","volume":"63","author":"N Neuman","year":"2013","unstructured":"Neuman N (2013) Inequalities and Bounds for the Incomplete Gamma Function. RM 63:1209\u20131214","journal-title":"RM"},{"key":"3594_CR18","doi-asserted-by":"crossref","unstructured":"Ludwin C (2011) Blood Alchohol Content. Undergraduate Journal of Mathematical Modeling: One + Two 2(3)","DOI":"10.5038\/2326-3652.3.2.1"},{"issue":"7\u20138","key":"3594_CR19","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1016\/j.camwa.2004.05.015","volume":"49","author":"JC Cort\u00e9s","year":"2005","unstructured":"Cort\u00e9s JC, Sevilla-Peris P, J\u00f3dar L (2005) Analytic-numerical approximating processes of diffusion equation with data uncertainty. Comput Math Appl 49(7\u20138):1255\u20131266. https:\/\/doi.org\/10.1016\/j.camwa.2004.05.015","journal-title":"Comput Math Appl"},{"key":"3594_CR20","first-page":"103","volume":"5","author":"SS Dragomir","year":"2000","unstructured":"Dragomir SS, Agarwal RP, Barnett NS (2000) Inequalities for Beta and Gamma functions via some classical and new integral inequalities. J Inequal Appl 5:103\u2013165","journal-title":"J Inequal Appl"},{"key":"3594_CR21","unstructured":"Bazhlekova E (2001) Fractional Evolution Equations in Banach spaces, Ph.D Thesis. Eindhoven University technology"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03594-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03594-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03594-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T05:39:00Z","timestamp":1780292340000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03594-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,16]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["3594"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03594-0","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,16]]},"assertion":[{"value":"14 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no potential Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"205"}}