ANALYSIS OF HIDDEN ATTRACTORS OF NON-EQUILIBRIUM FRACTAL-FRACTIONAL CHAOTIC SYSTEM WITH ONE SIGNUM FUNCTION

Lei Zhang, Shabir Ahmad (), Aman Ullah (), AKGÃœL Ali () and KARATAS AKGÃœL Esra ()
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Lei Zhang: Department of Mathematics, Hanshan Normal University, Chaozhou 521041 P. R. China
Shabir Ahmad: Department of Mathematics, University of Malakand, Chakdara Dir (L), 18800, Khyber Pakhtunkhwa, Pakistan
Aman Ullah: Department of Mathematics, University of Malakand, Chakdara Dir (L), 18800, Khyber Pakhtunkhwa, Pakistan
AKGÃœL Ali: Department of Mathematics, Art and Science Faculty, Siirt University, TR-56100 Siirt, Turkey
KARATAS AKGÃœL Esra: Department of Mathematics, Art and Science Faculty, Siirt University, TR-56100 Siirt, Turkey

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-16

Abstract: In 2017, Atangana proposed more generalized operators depending on two parameters: one is fractional order (FO) and other is fractal dimension. The novel operators are defined with three different kernels. These operators produced excellent dynamics of the chaotic systems. In this paper, the Caputo fractal-fractional operator is used to explore a chaotic system which contains only one signum function. The existence theory is developed by using the fixed-point result of Leray–Schauder to prove that the considered chaotic system possesses at least one solution. The proposed chaotic system has a unique solution, according to Banach’s fixed-point theorem. We demonstrate that the suggested chaotic system is Ulam–Hyres (UH) stable under the novel operator of power law kernel by employing nonlinear functional analysis. The Adams–Bashforth technique is used to evaluate the numerical outcomes of the considered model. We show the complex structure of numerical solutions for different FO and fractal dimension values.

Keywords: Signum Function; Chaotic System; Adams–Bashforth Method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401399

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