Some stability results for the fractional differential equations with two delays
Pragati Dutta, Sachin Bhalekar
Published: 2025/9/26
Abstract
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. Two cases are analyzed: one where the first delay is zero, and the second acts through an exponential coefficient, and another where the first delay is fixed. 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.