Stability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays

Date

2019-02-19

Authors

Hristova, Snezhana
Tunc, Cemil

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Publisher

Texas State University, Department of Mathematics

Abstract

We use Lyapunov functions to study stability of the first-order Volterra integro-differential equation with Caputo fractional derivative Ct0Dqtx(t) = -α(t)ƒ(x(t)) + ∫tt-r B(t, s)g(s, x(s))ds + h(t, x(t), x(t - τ(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.

Description

Keywords

fractional derivative, integro-differential equation, delay, Lyapunov functional, stability

Citation

Hristova, S., & Tunç, C. (2019). Stability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays. <i>Electronic Journal of Differential Equations, 2019</i>(30), pp. 1-11.

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Attribution 4.0 International

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