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System of fractional differential algebraic equations with applications

dc.contributor.authorShiri, B.
dc.contributor.authorBaleanu, Dumitru
dc.contributor.authorID56389tr_TR
dc.date.accessioned2020-02-28T12:18:26Z
dc.date.available2020-02-28T12:18:26Z
dc.date.issued2019
dc.departmentÇankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractOne of the important classes of coupled systems of algebraic, differential and fractional differential equations (CSADFDEs) is fractional differential algebraic equations (FDAEs). The main difference of such systems with other class of CSADFDEs is that their singularity remains constant in an interval. However, complete classifying and analyzing of these systems relay mainly to the concept of the index which we introduce in this paper. For a system of linear differential algebraic equations (DAEs) with constant coefficients, we observe that the solvability depends on the regularity of the corresponding pencils. However, we show that in general, similar properties of DAEs do not hold for FDAEs. In this paper, we introduce some practical applications of systems of FDAEs in physics such as a simple pendulum in a Newtonian fluid and electrical circuit containing a new practical element namely fractors. We obtain the index of introduced systems and discuss the solvability of these systems. We numerically solve the FDAEs of a pendulum in a fluid with three different fractional derivatives (Liouville-Caputo's definition, CaputoFabrizio's definition and with a definition with Mittag-Leffler kernel) and compare the effect of different fractional derivatives in this modeling. Finally, we solved some existing examples in research and showed the effectiveness and efficiency of the proposed numerical method. (C) 2019 Elsevier Ltd. All rights reserved.en_US
dc.description.publishedMonth3
dc.identifier.citationShiri, B.; Baleanu, D., "System of fractional differential algebraic equations with applications", Chaos Solitons & Fractals, Vol. 120, pp. 203-212, (2019).en_US
dc.identifier.doi10.1016/j.chaos.2019.01.028
dc.identifier.endpage212en_US
dc.identifier.issn0960-0779
dc.identifier.startpage203en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/2565
dc.identifier.volume120en_US
dc.language.isoenen_US
dc.publisherPergamon-Elsevier Science LTDen_US
dc.relation.ispartofChaos Solitons & Fractalsen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectSystem of Fractional Differential Equationsen_US
dc.subjectA Simple Pendulum in Newtonian Fluiden_US
dc.subjectMittag-Leffler Functionen_US
dc.subjectElectrical Circuits Containing Fractorsen_US
dc.subjectThe Index of Fractional Differential Algebraic Equationsen_US
dc.titleSystem of fractional differential algebraic equations with applicationstr_TR
dc.titleSystem of Fractional Differential Algebraic Equations With Applicationsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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