A new approach to the fractional Abel k-integral equations and linear fractional differential equations in a fuzzy environment

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dc.authoridAllahviranloo, Tofigh/0000-0002-6673-3560
dc.authoridVan Hoa, Ngo/0000-0002-4603-4682
dc.authorwosidAllahviranloo, Tofigh/V-4843-2019
dc.authorwosidVan Hoa, Ngo/K-7019-2014
dc.contributor.authorVan Hoa, Ngo
dc.contributor.authorAllahviranloo, Tofigh
dc.contributor.authorPedrycz, Witold
dc.date.accessioned2024-05-19T14:47:00Z
dc.date.available2024-05-19T14:47:00Z
dc.date.issued2024
dc.departmentİstinye Üniversitesien_US
dc.description.abstractThis paper introduces some recent approaches to the fuzzy fractional Abel integral equations with respect to another function, which is called the fuzzy fractional Abel k-integral equations. The problem proposed here allows for the interpolation of different types of fuzzy classical fractional Abel integral equations, and the solvability of each type of integral equation is also discussed. Additionally, a new approach to the linear fuzzy fractional differential equations in the space of generalized fuzzy functions is introduced. Unlike previous approaches with gH-differentiability, this approach avoids making any prior assumptions about the solution's monotonic behavior during the solving process. It also overcomes the problem of multiple solutions for fuzzy fractional differential equations. To demonstrate the benefits of this approach, two initial value problems of linear fuzzy differential equations are compared using two different concepts of fractional derivatives: the Caputo fractional gH-differentiability and the Caputo fractional derivative in the generalized fuzzy space. Furthermore, some applications are provided in a viscoelastic material model and a population growth with harvesting model.en_US
dc.identifier.doi10.1016/j.fss.2024.108895
dc.identifier.issn0165-0114
dc.identifier.issn1872-6801
dc.identifier.scopus2-s2.0-85185348959en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org10.1016/j.fss.2024.108895
dc.identifier.urihttps://hdl.handle.net/20.500.12713/5634
dc.identifier.volume481en_US
dc.identifier.wosWOS:001188991200001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofFuzzy Sets and Systemsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmz20240519_kaen_US
dc.subjectThe Fuzzy Fractional Abel K-Integral Equationsen_US
dc.subjectThe Linear Fuzzy Fractional Differential Equationsen_US
dc.subjectThe Generalized Fuzzy Spaceen_US
dc.subjectLaplace-Like Transformen_US
dc.subjectThe Pade Approximationen_US
dc.titleA new approach to the fractional Abel k-integral equations and linear fractional differential equations in a fuzzy environmenten_US
dc.typeArticleen_US

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