Controlled chaos of a fractal-fractional Newton-Leipnik system

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.