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Some qualitative properties of solutions to a nonlinear fractional differential equation involving two Φ-Caputo fractional derivatives

dc.contributor.authorDerbazi, Choukri
dc.contributor.authorAl-Mdallal, Qasem M.
dc.contributor.authorJarad, Fahd
dc.contributor.authorBaitiche, Zidane
dc.contributor.authorID234808tr_TR
dc.date.accessioned2024-05-14T11:14:41Z
dc.date.available2024-05-14T11:14:41Z
dc.date.issued2022
dc.departmentÇankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümüen_US
dc.description.abstractThe momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate of the solutions, the continuous dependence of the solutions on initial conditions and the existence and uniqueness of extremal solutions to a new class of fractional differential equations involving two fractional derivatives in the sense of Caputo fractional derivative with respect to another function Φ. Firstly, using the generalized Laplace transform method, we give an explicit formula of the solutions to the aforementioned linear problem which can be regarded as a novelty item. Secondly, by the implementation of the Φ-fractional Gronwall inequality, we analyze some properties such as estimates and continuous dependence of the solutions on initial conditions. Thirdly, with the help of features of the Mittag-Leffler functions (MLFs), we build a new comparison principle for the corresponding linear equation. This outcome plays a vital role in the forthcoming analysis of this paper especially when we combine it with the monotone iterative technique alongside facet with the method of upper and lower solutions to get the extremal solutions for the analyzed problem. Lastly, we present some examples to support the validity of our main results. © 2022 the Author(s), licensee AIMS Press.en_US
dc.identifier.citationDerbazi, Choukri...et al. "Some qualitative properties of solutions to a nonlinear fractional differential equation involving two Φ-Caputo fractional derivatives", AIMS Mathematics, Vol. 7, no. 6, pp. 9894-9910.en_US
dc.identifier.doi10.3934/math.2022552
dc.identifier.endpage9910en_US
dc.identifier.issn2473-6988
dc.identifier.issue6en_US
dc.identifier.startpage9894en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/8364
dc.identifier.volume7en_US
dc.language.isoenen_US
dc.relation.ispartofAIMS Mathematicsen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectExtremal Solutionsen_US
dc.subjectGeneralized Laplace Transformsen_US
dc.subjectMonotone Iterative Styleen_US
dc.subjectMulti-Termsen_US
dc.subjectUpper (Lower) Solutionsen_US
dc.subjectΦ-Caputo Fractional Derivativeen_US
dc.titleSome qualitative properties of solutions to a nonlinear fractional differential equation involving two Φ-Caputo fractional derivativestr_TR
dc.titleSome Qualitative Properties of Solutions To a Nonlinear Fractional Differential Equation Involving Two Φ-Caputo Fractional Derivativesen_US
dc.typeArticleen_US
dspace.entity.typePublication

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