Some stability results for the fractional differential equations with two delays

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal delays influence feedback mechanisms. In the first case, we set one of the delays to zero and analyzed the resulting system. We then extended the study to a more general case where both delays are allowed to vary. We derive delay-independent stability conditions using linearization, characteristic equations, and bifurcation theory, along with complete theoretical proofs. The results are validated through numerical simulations and stability diagrams.