Explicit analytical solutions of an incommensurate system of fractional differential equations in a fuzzy environment

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dc.authoridMuhammad, Ghulam/0009-0009-0422-7580
dc.authoridAllahviranloo, Tofigh/0000-0002-6673-3560
dc.authoridAkram, Muhammad/0000-0001-7217-7962
dc.authorwosidMuhammad, Ghulam/HLP-6635-2023
dc.authorwosidAllahviranloo, Tofigh/V-4843-2019
dc.authorwosidAkram, Muhammad/N-3369-2014
dc.contributor.authorAkram, Muhammad
dc.contributor.authorMuhammad, Ghulam
dc.contributor.authorAllahviranloo, Tofigh
dc.date.accessioned2024-05-19T14:41:42Z
dc.date.available2024-05-19T14:41:42Z
dc.date.issued2023
dc.departmentİstinye Üniversitesien_US
dc.description.abstractFuzzy fractional models have attracted considerable attention because of their comprehensive and broader understanding of real-world problems. Analytical studies of these models are often complex and difficult. Therefore, it is beneficial to develop a suitable and comprehensive technique to solve these models analytically. In this paper, an explicit analytical technique for solving two-dimensional incommensurate linear fuzzy systems of fractional Caputo differential equations (FLSoCFDEs) considering generalized Hukuhara differentiability (g H-differentiability) is presented and demonstrated. This extracted explicit solution is presented for different classes of such systems, including homogeneous and non-homogeneous cases with commensurate and incommensurate fractional orders. Moreover, the potential solution of FLSoCFDEs in terms of the Mittag-Leffler function involving double series is presented. The originality of the proposed technique is that the fuzzy Cauchy problem is transformed into a system of fuzzy linear Volterra integral equations of second kind and then the solution is extracted using the iterative Picard scheme based on the Banach fixed point theorem. Moreover, several interesting results are derived from FLSoCFDEs in terms of the Mittage-Leffler function for both homogeneous and inhomogeneous cases. To understand the proposed technique, we solve a diffusion process problem (a biological model) and several mass-spring systems as applications. Their graphs are analyzed to illustrate and support the theoretical results.en_US
dc.identifier.doi10.1016/j.ins.2023.119372
dc.identifier.issn0020-0255
dc.identifier.issn1872-6291
dc.identifier.scopus2-s2.0-85164219124en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org10.1016/j.ins.2023.119372
dc.identifier.urihttps://hdl.handle.net/20.500.12713/5147
dc.identifier.volume645en_US
dc.identifier.wosWOS:001040812300001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevier Science Incen_US
dc.relation.ispartofInformation Sciencesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmz20240519_kaen_US
dc.subjectFuzzy Caputo G H-Fractional Derivativeen_US
dc.subjectTwo-Dimensional Incommensurate Fuzzy Linearen_US
dc.subjectSystems Of Caputo Fractional Differentialen_US
dc.subjectEquationsen_US
dc.subjectMittag-Leffler Function Involving Double Seriesen_US
dc.subjectCommensurate And Incommensurate Fractionalen_US
dc.subjectOrderen_US
dc.titleExplicit analytical solutions of an incommensurate system of fractional differential equations in a fuzzy environmenten_US
dc.typeArticleen_US

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