ABSTRACT
In this study, fractal-fractional derivatives (FFD) with exponential decay laws kernels are applied to explain the chaotic behavior of a Newton-Leipnik system (NLS) with constant and time-varying derivatives. By using Caputo-Fabrizio fractal-fractional derivatives, fixed point theory verifies their existence and uniqueness. Using the implicit finite difference method, the Caputo-Fabrizio (CF) FF NLS is numerically solved. There are several numerical examples presented to illustrate the method's applicability and efficiency. The CF fractal-fractional solutions are more general as compared to classical solutions, as shown in the graphics. Three parameters, three quadratic non-linearity, low complexity time, short iterations per second, a larger step size for the discretized version where chaos is preserved, low cost electronic implementation, and flexibility are some of the unique features that make the suggested chaotic system novel.
KEYWORDS
PAPER SUBMITTED: 2024-06-02
PAPER REVISED: 2024-10-21
PAPER ACCEPTED: 2024-11-01
PUBLISHED ONLINE: 2025-01-25
THERMAL SCIENCE YEAR
2024, VOLUME
28, ISSUE
Issue 6, PAGES [5153 - 5160]
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