RANDOM ATTRACTOR FOR STOCHASTIC PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

The Asymptotic Behavior for Second-Order Neutral Stochastic Partial Differential Equations with Infinite Delay

Stability results for impulsive functional differential equations with infinite delay

For a family of differential equations with infinitive delay and impulses, we establish conditions for the existence of global solutions and for the global asymptotic and global exponential stabilities of an equilibrium point. The results are used to give stability criteria for a very broad family of impulsive neural network models with both unbounded distributed delays and bounded time-varying...

Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps

and Applied Analysis 3 (H3) There exists L 2 > 0 satisfying 󵄩󵄩󵄩h(x, y, u) 󵄩󵄩󵄩 2 H ≤ L 2 (‖x‖ 2 H + 󵄩󵄩󵄩y 󵄩󵄩󵄩 2 H ) , (12) for each x, y ∈ H and u ∈ Z. (H4) For ξ ∈ Db F0 0],H), there exists a constantL3 > 0 such that E ( 󵄨󵄨󵄨ξ (s) − ξ (t) 󵄨󵄨󵄨 2 ) ≤ L 3 |t − s| 2 , t, s ∈ [−τ, 0] . (13) We now describe our Euler-Maruyama scheme for the approximation of (1). For any n ≥ 1, let π n : H → H n = span{...