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.
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