Résumé:
The fractional order differential and fractional order difference systems were the primary topics of
this research. A linear control rule for stabilizing the fractional discrete-time Ushio system that is
based on the Lyapunov method and Caputo h-difference operator's characteristics is first proposed.
The study is accompanied by numerical results that serve to demonstrate the conclusions. A
qualitative description of the Halvorsen circulant system (HCS) with a fractional-order Caputo
derivative is then provided. We also study the stabilization and synchronization of identical FO-HCS
and provide a numerical solution for this system using the Adomian decomposition technique (ADM).
Furthermore, the approach for encrypting images using extended fractional sequences was
developed by using the exceptional qualities of the fractional-order system. Lastly, it is effective and
secure in picture data, as shown by the simulation results and its performance.
