Contribution in fractional derivative order dynamic models

Abstract

This thesis focuses on the study of linear or nonlinear dynamic systems either of order fractional or on time scales or both. The aim of study on the one hand, Proof the existence and uniqueness of initial value problem of Riemann-Liouville fractional order on time scales using fixed point theorems. Then, presentation of the exact solution to a general Norton Massagué Model on time scales with exam- ples. On the other hand, we study the stability of SAIQH Models on time scales and we prove that the system is permanent. Finally, we introduce a fractional order SAIRS model and we prove the existence and the positivity of solution, then we discuss the loacal and global stability of the system.