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Asymptotic solutions of fractional interval differential equations with nonsingular kernel derivative

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dc.contributor.author Salahshour, S.
dc.contributor.author Ahmadian, Ali
dc.contributor.author Salimi, M.
dc.contributor.author Ferrara, M.
dc.contributor.author Baleanu, Dumitru
dc.date.accessioned 2020-02-12T07:11:53Z
dc.date.available 2020-02-12T07:11:53Z
dc.date.issued 2019-08
dc.identifier.citation Salahshour, S...et al. (2019). "Asymptotic solutions of fractional interval differential equations with nonsingular kernel derivative", Chaos, Vol. 29, No. 8. tr_TR
dc.identifier.issn 1054-1500
dc.identifier.uri http://hdl.handle.net/20.500.12416/2421
dc.description.abstract Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters. Published under license by AIP Publishing. tr_TR
dc.language.iso eng tr_TR
dc.publisher Amer Inst Physics tr_TR
dc.relation.isversionof 10.1063/1.5096022 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Valued Functions tr_TR
dc.subject Integral-Equations tr_TR
dc.subject Tau Method tr_TR
dc.subject Stability tr_TR
dc.subject Calculus tr_TR
dc.subject Order tr_TR
dc.subject Behavior tr_TR
dc.subject Models tr_TR
dc.title Asymptotic solutions of fractional interval differential equations with nonsingular kernel derivative tr_TR
dc.type article tr_TR
dc.relation.journal Chaos tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 29 tr_TR
dc.identifier.issue 8 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik - Bilgisayar Bölümü tr_TR


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