On the uniform asymptotic stability for a linear integro-differential equation of Volterra type

Asymptotic Stability Analysis of a Stochastic Volterra Integro-differential Equation with Fading Memory

We investigate the long term behavior of solutions to a stochastic Volterra integro-differential equation with a fading memory; the fading memory is represented by using a decaying exponential convolution kernel. We give sufficient conditions for asymptotic mean square stability of the solution. In a similar spirit, we investigate the long term behavior of solutions to discrete analogues of the...

An Integro-differential Equation of Volterra Type with Sumudu Transform

In this paper a closed form solution of a fractional integro-differential equation of Volterra type involving Mittag-Leffler function has been obtained using straight forward technique of Sumudu transform. Some particular cases have also been considered.

Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation

We consider the system of Volterra integro-dynamic equations x(t) = A(t)x(t) + ∫ t t0 B(t, s)x(s)∆s and obtain necessary and sufficient conditions for the uniform stability of the zero solution employing the resolvent equation coupled with the variation of parameters formula. The resolvent equation that we use for the study of stability will have to be developed since it is unknown for time sca...

Approximation the fuzzy solution of the non linear fuzzy Volterra integro differential equation using fixed point theorems

Global Stability for a Nonlinear Volterra Integro–Differential System

Sufficient conditions are given which guarantee that the trivial solution x = 0 for a nonlinear integro–differential system is globally attracting. As an example, this result is applied to a SIRS epidemic model with subpopulations to show that, under certain conditions, the endemic equilibrium is globally asymptotically stable.