Analysis of a Lorenz model using adomian decomposition and fractal-fractional operators
Yan Tao, Muflih Alhazmi, Mukhtar Yagoub Youssif, Amna E. Elhag, A. F. Aljohani, Sayed Saber
Abstract
This paper extends the classical Lorenz system to incorporate fractal-fractional dynamics, providing a detailed numerical analysis of its chaotic behavior. By applying Caputo's fractal-fractional operators to the Lorenz system, the study explores the fractal and fractional nature of non-linear systems. Numerical methods are employed to solve the extended system, with suitable fractal and fractional orders chosen to demonstrate chaos and hyper-chaos. The results are presented graphically, highlighting the complex dynamic behavior of the system under different parameter conditions. This research advances the understanding of fractional calculus in modelling and controlling chaotic systems in various scientific fields.