Aggoun, ChaymaRouar, Salim2024-10-152024-10-152024http://dspace.univ-oeb.dz:4000/handle/123456789/19972This memory is concerned with studying the behavior of chaotic and hyper-chaotic dynamic systems with fractional derivatives and making them stable. We relied on the Lyapunov foundation method and the stability criterion to detect chaos. Then we addressed the issue of control by relying on feedback control and/or synchronization of this chaotic behavior to make it stable. All results of the theory studied in this note have been confirmed using software simulations. The obtained results were confirmed using the MATLAB program.enStability; Lyapunov exponents; Fractional derivatives