Stability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays
Date
2019-02-19
Authors
Hristova, Snezhana
Tunc, Cemil
Journal Title
Journal ISSN
Volume Title
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.
Rights
Attribution 4.0 International