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Dynamics of chaotic system based on image encryption through fractal-fractional operator of non-local kernel

Authors :
Naveed Khan
Zubair Ahmad
Hijaz Ahmad
Fairouz Tchier
Xiao-Zhong Zhang
Saqib Murtaza
Source :
AIP Advances, Vol 12, Iss 5, Pp 055129-055129-17 (2022)
Publication Year :
2022
Publisher :
AIP Publishing LLC, 2022.

Abstract

In this paper, the newly developed fractal-fractional differential and integral operators are used to analyze the dynamics of chaotic system based on image encryption. The problem is modeled in terms of classical order nonlinear, coupled ordinary differential equations that are then generalized through fractal-fractional differential operator of Mittag-Leffler kernel. In addition to that, some theoretical analyses, such as model equilibria, existence, and uniqueness of the solutions, have been proved. Furthermore, the highly non-linear problem is solved by adopting a numerical scheme through MATLAB software. The graphical solution is portrayed through 2D and 3D portraits. Some interesting results are concluded considering the variation of fractional-order parameter and fractal dimension parameter.

Subjects

Subjects :
Physics
QC1-999

Details

Language :
English
ISSN :
21583226
Volume :
12
Issue :
5
Database :
Directory of Open Access Journals
Journal :
AIP Advances
Publication Type :
Academic Journal
Accession number :
edsdoj.f4b59d34e45d6b121e332b9a69361
Document Type :
article
Full Text :
https://doi.org/10.1063/5.0085960