Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator
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Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Pergamon-Elsevier Science Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A 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.
Açıklama
Anahtar Kelimeler
Fractal-fractional operator, Chaotic dynamical system, Ulam-Hyres stability, Fractal dimension, Primary 26a33, Secondary 34a08
Kaynak
Chaos Solitons & Fractals
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
146
