Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator

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dc.authoridUllah, Aman/0000-0003-4021-3599
dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.contributor.authorAhmad, Shabir
dc.contributor.authorUllah, Aman
dc.contributor.authorAkgul, Ali
dc.date.accessioned2024-12-24T19:25:26Z
dc.date.available2024-12-24T19:25:26Z
dc.date.issued2021
dc.departmentSiirt Üniversitesi
dc.description.abstractA new set of differential and integral operators has recently been proposed by Abdon et al., merging the fractional derivative and the fractal derivative, taking into account non-locality, memory and fractal effects. These operators have demonstrated the complex behaviour of many physical phenomena, which generally does not predict in ordinary operators or sometimes also in fractional operators. In this article, we investigate a three dimensional quadratic multi scroll chaotic dynamical system under Caputo fractal-fractional operator. We study the proposed model by replacing the fractional derivative by fractalfractional derivatives based on Caputo. Through Schauder?s fixed point theorem, we establish existence theory to ensure that the model possesses at least one solution. Also, Banach fixed theorem guarantees the uniqueness of solution of the proposed model. By mean of non-linear functional analysis, we derive that the proposed model is Ulam-Hyres stable under the new fractal-fractional derivative. We establish the numerical scheme of the considered model through Lagrangian piece-wise interpolation. For the different values of fractional order and fractal dimension, we present the complex behaviour of the proposed model. ? 2021 Elsevier Ltd. All rights reserved.
dc.identifier.doi10.1016/j.chaos.2021.110900
dc.identifier.issn0960-0779
dc.identifier.issn1873-2887
dc.identifier.scopus2-s2.0-85103690767
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.chaos.2021.110900
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6410
dc.identifier.volume146
dc.identifier.wosWOS:000647560700005
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherPergamon-Elsevier Science Ltd
dc.relation.ispartofChaos Solitons & Fractals
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectFractal-fractional operator
dc.subjectChaotic dynamical system
dc.subjectUlam-Hyres stability
dc.subjectFractal dimension
dc.subjectPrimary 26a33
dc.subjectSecondary 34a08
dc.titleInvestigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator
dc.typeArticle

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