CHAOTIC BEHAVIOR OF BHALEKAR-GEJJI DYNAMICAL SYSTEM UNDER ATANGANA-BALEANU FRACTAL FRACTIONAL OPERATOR

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dc.authoridAhmad, Shabir/0000-0002-5610-6248
dc.authoridUllah, Aman/0000-0003-4021-3599
dc.contributor.authorAhmad, Shabir
dc.contributor.authorUllah, Aman
dc.contributor.authorAkgul, Ali
dc.contributor.authorAbdeljawad, Thabet
dc.date.accessioned2024-12-24T19:29:41Z
dc.date.available2024-12-24T19:29:41Z
dc.date.issued2022
dc.departmentSiirt Üniversitesi
dc.description.abstractIn this paper, a new set of differential and integral operators has recently been proposed by Abdon et al. by merging the fractional derivative and the fractal derivative, taking into account nonlocality, memory and fractal effects. These operators have demonstrated the complex behavior of many physical, which generally does not predict in ordinary operators or sometimes in fractional operators also. In this paper, we investigate the proposed model by replacing the classic derivative by fractal-fractional derivatives in which fractional derivative is taken in Atangana-Baleanu Caputo sense to study the complex behavior due to nonlocality, memory and fractal effects. Through Schauder's fixed point theorem, we establish existence theory to ensure that the model posseses at least one solution. Also, Banach fixed theorem guarantees the uniqueness of solution of the proposed model. By means of nonlinear functional analysis, we prove that the proposed model is Ulam-Hyers stable under the new fractal-fractional derivative. We establish the numerical results of the considered model through Lagrangian piece-wise interpolation. For the different values of fractional order and fractal dimension, we study the chaos behavior of the proposed model via simulation at 2D and 3D phase. We show the effect of fractal dimension on integer and fractional order through simulations.
dc.identifier.doi10.1142/S0218348X22400059
dc.identifier.issn0218-348X
dc.identifier.issn1793-6543
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85116845536
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1142/S0218348X22400059
dc.identifier.urihttps://hdl.handle.net/20.500.12604/7209
dc.identifier.volume30
dc.identifier.wosWOS:000766635200031
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherWorld Scientific Publ Co Pte Ltd
dc.relation.ispartofFractals-Complex Geometry Patterns and Scaling in Nature and Society
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectFractal-Fractional Operator
dc.subjectBhalekar-Gejji Dynamical System
dc.subjectUlam-Hyers Stability
dc.titleCHAOTIC BEHAVIOR OF BHALEKAR-GEJJI DYNAMICAL SYSTEM UNDER ATANGANA-BALEANU FRACTAL FRACTIONAL OPERATOR
dc.typeArticle

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