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

Shabir Ahmad, Aman Ullah and Ali Akgül

Chaos, Solitons & Fractals, 2021, vol. 146, issue C

Abstract: 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 fractal-fractional 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.

Keywords: Fractal-fractional operator; Chaotic dynamical system; Ulam-Hyres stability; Fractal dimension; Primary 26a33; Secondary 34a08; 35R11 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007792100254X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:146:y:2021:i:c:s096007792100254x

DOI: 10.1016/j.chaos.2021.110900

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().