Dynamics of chaotic system based on image encryption through fractal-fractional operator of non-local kernel
Naveed Khan,
Zubair Ahmad,
Hijaz Ahmad,
Fairouz Tchier,
Xiao-Zhong Zhang,
Saqib Murtaza
Affiliations
Naveed Khan
Department of Mathematics, City University of Science and Information Technology, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan
Zubair Ahmad
Dipartimento di Matematica e Fisica, Universit‘a degli Studi della Campania “Luigi Vanvitelli,” Caserta 81100, Italy
Hijaz Ahmad
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39,00186 Roma, Italy
Fairouz Tchier
Department of Mathematics, King Saud University, Riyadh 145111, Saudi Arabia
Xiao-Zhong Zhang
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
Saqib Murtaza
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
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.
