TY - JOUR
TI - Numerical approximation method and chaos for a chaotic system in sense of Caputo-Fabrizio operator
AU - Alhazmi Muflih
AU - Dawalbait Fathi M
AU - Aljohani Abdulrahman F
AU - Taha Khdija O
AU - Adam Haroon D.S.
AU - Saber Sayed
JN - Thermal Science
PY - 2024
VL - 28
IS - 6
SP - 5161
EP - 5168
PT - Article
AB - This paper presents a novel numerical method for analvwing chaotic systems,  focusing on applications to real-world problems. The Caputo-Fabrizio  operator, a fractional derivative without a singular kernel, is used to  investigate chaotic behavior. A fractional-order chaotic model is analvwed  using numerical solutions derived from this operator, which captures the  complexity of chaotic dynamics. In this paper, the uniqueness and  boundedness of the solution are established using fixed-point theory. Due to  the non-linearity of the system, an appropriate numerical scheme is  developed. We further explore the model's dynamical properties through  phase portraits, Lyapunov exponents, and bifurcation diagrams. These tools  allow us to observe the system’s sensitivity to varying parameters and  derivative orders. Ultimately, this work extends the application of  fractional calculus to chaotic systems and provides a robust methodology for  obtaining insights into complex behaviors.