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dc.contributor.authorAllahviranloo, Tofigh
dc.contributor.authorNoeiaghdam, Zahra
dc.contributor.authorNoeiaghdam, Samad
dc.contributor.authorNieto Roig, Juan José
dc.date.accessioned2020-12-16T12:36:03Z
dc.date.available2020-12-16T12:36:03Z
dc.date.issued2020
dc.identifier.citationAllahviranloo, T.; Noeiaghdam, Z.; Noeiaghdam, S.; Nieto, J.J. A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion. Mathematics 2020, 8, 2166
dc.identifier.urihttp://hdl.handle.net/10347/24014
dc.description.abstractIn this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations using fuzzy calculations and without this transformation. In this work, the fuzzy generalized Taylor expansion by using the sense of fuzzy Caputo fractional derivative for fuzzy-valued functions is presented. For solving fuzzy fractional differential equations, the fuzzy generalized Euler’s method is introduced and applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, convergence, and stability of the generalized Euler’s method are proved in detail. Eventually, the numerical examples, especially in the switching point case, show the flexibility and the capability of the presented method
dc.description.sponsorshipThe work of J.J. Nieto has been partially supported by Agencia Estatal de Investigación (AEI) of Spain under grant MTM2016-75140-P, co-financed by the European Community fund FEDER, and XUNTA de Galicia under grants GRC2015-004 and ED431C 2019/02
dc.language.isoeng
dc.publisherMDPI
dc.relationinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-75140-P/ES
dc.rights© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)
dc.rightsAtribución 4.0 Internacional
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectFuzzy fractional differential equations
dc.subjectGeneralized fuzzy Taylor expansion
dc.subjectGeneralized fuzzy Euler’s method
dc.subjectGlobal truncation error
dc.subjectLocal truncation error
dc.subjectConvergence
dc.subjectStability
dc.titleA Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion
dc.typeinfo:eu-repo/semantics/article
dc.identifier.DOI10.3390/math8122166
dc.relation.publisherversionhttps://doi.org/10.3390/math8122166
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.identifier.e-issn2227-7390
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
dc.description.peerreviewedSI


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© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)
Except where otherwise noted, this item's license is described as  © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)





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