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Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density

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Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density

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dc.contributor.author Burgos, C. es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Villafuerte, L. es_ES
dc.contributor.author Villanueva Micó, Rafael Jacinto es_ES
dc.date.accessioned 2021-02-19T04:33:26Z
dc.date.available 2021-02-19T04:33:26Z
dc.date.issued 2020-11 es_ES
dc.identifier.issn 0377-0427 es_ES
dc.identifier.uri http://hdl.handle.net/10251/161842
dc.description.abstract [EN] A fractional forward Euler-like method is developed to solve initial value problems with uncertainties formulated via the Caputo fractional derivative. The analysis is conducted by using the so-called random mean square calculus. Under mild conditions on the data, the mean square convergence of the numerical method is proved. This type of stochastic convergence guarantees the approximations of the mean and the variance of the solution stochastic process, computed via the aforementioned numerical scheme, will converge to their corresponding exact values. Furthermore, from this probability information, we calculate reliable approximations to the first probability density function of the solution by taking advantage of the Maximum Entropy Principle. The theoretical analysis is illustrated by two examples. es_ES
dc.description.sponsorship This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P and by the European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 20142020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Journal of Computational and Applied Mathematics es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Fractional differential equations with randomness es_ES
dc.subject Random mean square calculus es_ES
dc.subject Random mean square Caputo fractional derivative es_ES
dc.subject Random numerics es_ES
dc.subject Maximum Entropy Principle es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.cam.2020.112925 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-89664-P/ES/PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//GJIDI%2F2018%2FA%2F009/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//GJIDI%2F2018%2FA%2F010/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Multidisciplinar - Institut Universitari de Matemàtica Multidisciplinària es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Burgos, C.; Cortés, J.; Villafuerte, L.; Villanueva Micó, RJ. (2020). Mean square convergent numerical solutions of random fractional differential equations: Approximations of moments and density. Journal of Computational and Applied Mathematics. 378:1-14. https://doi.org/10.1016/j.cam.2020.112925 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1016/j.cam.2020.112925 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 14 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 378 es_ES
dc.relation.pasarela S\406996 es_ES
dc.contributor.funder European Social Fund es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
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