Incommensurate non-homogeneous system of fuzzy linear fractional differential equations using the fuzzy bunch of real functions

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dc.authoridAllahviranloo, Tofigh/0000-0002-6673-3560
dc.authoridMuhammad, Ghulam/0009-0009-0422-7580
dc.authoridAkram, Muhammad/0000-0001-7217-7962
dc.authorwosidAllahviranloo, Tofigh/V-4843-2019
dc.authorwosidMuhammad, Ghulam/HLP-6635-2023
dc.authorwosidAkram, Muhammad/N-3369-2014
dc.contributor.authorAkram, Muhammad
dc.contributor.authorMuhammad, Ghulam
dc.contributor.authorAllahviranloo, Tofigh
dc.contributor.authorPedrycz, Witold
dc.date.accessioned2024-05-19T14:41:43Z
dc.date.available2024-05-19T14:41:43Z
dc.date.issued2023
dc.departmentİstinye Üniversitesien_US
dc.description.abstractThis article aims to introduce and investigate the analytical fuzzy solution of the incommensurate non-homogeneous system of fuzzy linear fractional differential equations (INS-FLFDEs) using trivariate Mittag-Leffler functions. Entries of the coefficient matrix of the given system are treated as real numbers, initial-values are triangular fuzzy numbers (TFNs), and the forcing function is a fuzzy set (or a bunch) of real function. We extract the potential solution in the form of a fuzzy bunch of real functions (FBoRFs) rather than the solution of fuzzy-valued functions. We formulate the fuzzy initial value problem as a set of classical initial value problems by taking the forcing function from the class of FBoRFs and the initial value from the collection of TFNs (as a special case). The solution of this system is in the form of a trivariate Mittag-Leffler function. We interpret this solution as an element of the fuzzy solution set and assign the minimum value of membership that takes from the forcing function and the initial value in the fuzzy set. The originality of the proposed technique is that the uncertainty is smaller compared to the uncertainty extracted from other techniques. In addition, generalized derivatives increase the order and dimension of the system. Therefore, the proposed technique is better in terms of complexity because it reduces the order and dimension of the system. Finally, to grasp the proposed technique, we solve the electrical network and multiple mass-spring systems as applications and analyze their graphs to visualize and support theoretical results.en_US
dc.identifier.doi10.1016/j.fss.2023.108725
dc.identifier.issn0165-0114
dc.identifier.issn1872-6801
dc.identifier.scopus2-s2.0-85173575324en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.urihttps://doi.org10.1016/j.fss.2023.108725
dc.identifier.urihttps://hdl.handle.net/20.500.12713/5150
dc.identifier.volume473en_US
dc.identifier.wosWOS:001096950500001en_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.subjectFuzzy Linear Fractional Differential Equationsen_US
dc.subjectCaputo Fractional Derivativeen_US
dc.subjectFuzzy Bunch Of Real Functionsen_US
dc.subjectTrivariate Mittag-Leffler Functionen_US
dc.titleIncommensurate non-homogeneous system of fuzzy linear fractional differential equations using the fuzzy bunch of real functionsen_US
dc.typeArticleen_US

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