Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

Asymptotic Self-similarity for Solutions of Partial Integrodifferential Equations

The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are identified and are shown to actually occur. The limiting equations are fractional diffusion equations which are known to have self-similar fundamental solutions. F...

Lyapunov stability solutions of fractional integrodifferential equations

Lyapunov stability and asymptotic stability conditions for the solutions of the fractional integrodiffrential equations x (α) (t) = f (t, x(t)) + t t 0 K(t, s, x(s))ds, 0 < α ≤ 1, with the initial condition x (α−1) (t 0) = x 0 , have been investigated. Our methods are applications of Gronwall's lemma and Schwartz inequality.

Solutions to stochastic fractional oscillation equations

We formulate a fractional stochastic oscillation equation as a generalization of Bagley’s fractional differential equation. We do this in analogous way as in the case of Basset’s equation which gives rise to fractional stochastic relaxation equations. We analyze solutions under some conditions of spatial regularity of the operators considered.

On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space

Asymptotic Solutions of Semilinear Stochastic Wave Equations

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponenti...