Stability of scalar nonlinear fractional differential equations with linearly dominated delay

Hoang The Tuan
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  • Institute of Mathematics Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam
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and Stefan Siegmund

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.

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Fractional Calculus and Applied Analysis (FCAA) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order.

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