Browsing by Author "Hristova, Snezhana"

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    Conference Object
    On the Stability Properties of Retarded Volterra Integro-Fractional Differential Equations With Caputo Derivative
    (Amer inst Physics, 2021) Hristova, Snezhana; Tunc, Cemil
    In this paper, the direct Lyapunov method is extended to fractional case of Volterra integro-Caputo fractional differential equations with delays. Two types of homogeneous scalar Voterra integro-Caputo fractional differential equations with delays are studied. Three types of fractional derivatives of Lyapunov functions known in the literature are given. Uniform stability of trivial solution of that retarded IFrDEs is investigated using the Razumikhin method and different types of fractional derivatives of Lyapunov functions. Examples to show the application of the theorems are provided.
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    Article
    Stability of Nonlinear Volterra Integro-Differential Equations With Caputo Fractional Derivative and Bounded Delays
    (Texas State Univ, 2019) Hristova, Snezhana; Tunc, Cemil
    We use Lyapunov functions to study stability of the first-order Volterra integro-differential equation with Caputo fractional derivative (C)(t0)D(t)(q)x(t) = -a(t)f(x(t)) + integral(t-r) (t) B(t, s)g(s, x(s))ds + h(t, x(t), x(t-tau(t))). For the Lyapunov functions, we consider three types of fractional derivatives. By means of these derivatives, we obtain new sufficient conditions for stability and uniformly stability of solutions We consider both constant and time variable bounded delays, and illustrated our results with an example.