TY - JOUR
TI - Controlled chaos of a fractal-fractional Newton-Leipnik system
AU - Alsulami Amer
AU - Alharb Rasmiyah A
AU - Albogami Tahani M
AU - Eljaneid Nidal H.e
AU - Adam Haroon D.S.
AU - Saber Sayed
JN - Thermal Science
PY - 2024
VL - 28
IS - 6
SP - 5153
EP - 5160
PT - Article
AB - 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.