الفهرس 
IntroductionOnly 14 pages are availabe for public view
 |  | from | 108 |  |  |
| | | from | 108 | | |
Abstract
This thesis contributes to understanding the dynamics of fractional-order differential equations with two different delays. We proposed two models: the fractional-order logistic equation with two different delays and the fractional-order Nicholson equation with two different delays. We studied the stability regions by using the critical curves method. We explored how the fractional order $\alpha$, constant parameters, and time delays influence the stability and Hopf bifurcation of the two models. By choosing constant parameters, fractional order α and time delays as a bifurcation parameters, the delay bifurcation curve for the emergence of the Hopf bifurcation is determined. An Adams-type predictor-corrector method is extended to solve fractional-order differential equations involving two different delays.
Finally, numerical simulations are given to illustrate the effectiveness and feasibility of the theoretical results.
We obtained the following results:
1. The stability region is located between the vertical axis (when the time delay equals zero) and the Hopf bifurcation curve.
2. The stability regions and critical curves are sensitive to the fractional order, constant parameters, and time delays.
3. The bifurcation point and critical surfaces for different fractional orders and constant parameters have been illustrated.
4. Our results are confirmed by numerical simulations.