Stability of scalar nonlinear fractional differential equations with linearly dominated delay

TL;DR

This paper investigates the stability of scalar fractional delay differential equations, establishing conditions for asymptotic stability and demonstrating its robustness under small nonlinear perturbations.

Contribution

It provides new criteria for stability in fractional delay equations and shows stability preservation under nonlinear Lipschitz perturbations.

Findings

Conditions for asymptotic stability of linear fractional delay equations

Stability preservation under small nonlinear Lipschitz perturbations

Analysis of solutions near equilibrium points

Abstract

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay equation is asymptotically stable and show that the asymptotic stability of the trivial solution is preserved under a small nonlinear Lipschitz perturbation of the fractional delay differential equation.