Neutral Stochastic Functional Integro-differential Equations Research Articles

Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by fBm with Noncompact Semigroup via Mönch Fixed Point

Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by fBm with Noncompact Semigroup via Mönch Fixed Point

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

Asymptotic properties of solutions for impulsive neutral stochastic functional integro-differential equations

In this work, we are concerned with the asymptotic properties of solutions for an impulsive neutral stochastic functional integro-differential equation. By applying the theory of resolvent operators, the Banach fixed point principle theorem, and results on stochastic analysis, we study respectively the existence, uniqueness, and global attracting and quasi-invariant sets of mild solutions for the considered equation. We also derive some sufficient conditions of pth moment exponential stability and almost surely exponential stability of the mild solutions. An example is provided in the end to illustrate the applications of the obtained results.

Controllability of neutral stochastic functional integro-differential equations driven by fractional brownian motion with Hurst parameter lesser than $ 1/2 $

<p style='text-indent:20px;'>This article investigates the controllability for neutral stochastic delay functional integro-differential equations driven by a fractional Brownian motion, with Hurst parameter lesser than <inline-formula><tex-math id="M2">\begin{document}$ 1/2 $\end{document}</tex-math></inline-formula>. We employ the theory of resolvent operators developed by [<xref ref-type="bibr" rid="b10">10</xref>] combined with the Banach fixed point theorem to establish sufficient conditions to prove the desired result.</p>

Attractiveness and Exponential p-Stability of Neutral Stochastic Functional Integrodifferential Equations Driven by Wiener Process and fBm with Impulses Effects

In this work, we consider a class of neutral stochastic integro-differential equations driven by Wiener process and fractional Brownian motion with impulses effects. This paper deals with the global attractiveness and quasiinvariant sets for neutral stochastic integro-differential equations driven by Wiener process and fractional Brownian motion with impulses effects in Hilbert spaces. We use new integral inequalities combined with theoriesof resolvent operators to establish a set of sufficient conditions for the exponential p-stability of the mild solution of the considered equations. An example is presented to demonstrate the obtained theory.

Stability for some impulsive neutral stochastic functional integro-differential equations driven by fractional Brownian motion

The aim of this work is to study the stability for some integro-differential equations with impulses driven by fractional Brownian motion with noncompact semigroup in Hilbert spaces. We assume that...

Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.

Controllability for neutral stochastic functional integrodifferential equations with infinite delay

Abstract In this work, we study the controllability for a class of nonlinear neutral stochastic functional integrodifferential equations with infinite delay in a real separable Hilbert space. Sufficient conditions for the controllability are established by using Nussbaum fixed point theorem combined with theories of resolvent operators. As an application, an example is provided to illustrate the obtained result.

Controllability of neutral stochastic functional integro-differential equations driven by fractional Brownian motion

ABSTRACTThis article focuses on controllability results of neutral stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators developed by Grimmer [Resolvent operators for integral equations in Banach spaces, Trans. Amer. Math. Soc., 273(1982):333–349] combined with a fixed point approach for achieving the required result. An example is provided to illustrate the theory.

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

Impulsive neutral stochastic functional integro-differential equations with infinite delay driven by fBm

In this paper, we study a class of impulsive neutral stochastic functional integro-differential equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion (fBm) with Hurst parameter H∈(1/2,1) in the Hilbert space. We prove the existence and uniqueness of the mild solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions, which include the classical Lipschitz conditions as special case. An example is provided to illustrate the theory. Some well-known results are generalized and extended.

Existence results for impulsive neutral stochastic functional integrodifferential systems with infinite delay

This paper is devoted to build the existence of mild solutions of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) with infinite delay at abstract phase space in Hilbert spaces. Under the uniform Lipschitz condition, we obtain the solution for INSFIDEs. Sufficient conditions for the existence results are derived with the help of Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the theory.

Existence Results for Impulsive Neutral Stochastic Functional Integro-Differential Equations with Infinite Delays

In this paper, we prove the existence of mild solutions for a class of impulsive neutral stochastic functional integro-differential equations with infinite delays in an abstract space by means of the Krasnoselskii-Schaefer type fixed point theorem.

Controllability for Neutral Stochastic Functional Integrodifferential Infinite Delay Systems in Abstract Space

In this paper, sufficient conditions are given for the controllability of a class of neutral stochastic functional integrodifferential equations with infinite delay in abstract space. The Nussbaum fixed point theorem is adapted to obtain the controllability results, which greatly extends the previous results to the stochastic settings with the help of analytic semigroups. An example is provided to illustrate the theory.