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

Controllability of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay via resolvent operator

This paper is concerned with the controllability results of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, the theory of resolvent operator in the sense of Grimmer and Krasnoselskii fixed point theorem. An example is provided to illustrate the obtained theory.

Controllability of impulsive stochastic functional integrodifferential equations driven by Rosenblatt process and Lévy noise

In this paper, we develop controllability findings for impulsive neutral stochastic delay partial integrodifferential equations in Hilbert spaces driven by Rosenblatt process and Lévy noise. A novel set of adequate requirements is obtained by utilizing a fixed point method without imposing a stringent compactness constraint on the semigroup. The observed results represent a generalization and continuation of previous findings on this topic. Finally, an example is given to demonstrate how the acquired findings may be used.

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.

Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays

In this article, we concentrate on the existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays. Initially, the existence of the mild solutions to the equations by utilizing Banach fixed point theorem is demonstrated. In the later case we explore the Hyers Ulam stability results under the Lipschitz condition on a bounded and closed interval.

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.

Existence and stability results for stochastic functional integro-differential equations with poisson jumps under non-Lipschitz conditions

Existence and stability results for stochastic functional integro-differential equations with poisson jumps under non-Lipschitz conditions

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...

Existence and Stability Results for Impulsive Stochastic Functional Integrodifferential Equation with Poisson Jumps

In this article we present the existence, uniqueness and stability of mild solutions for impulsive stochastic functional integro differential equations with non-Lipschitz condition. The mild solution is obtained by using a resolvent operator in a different sense and the results are proved by using the method of successive approximation and Bihari’s inequality.

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.

Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior

Abstract This paper deals with the existence and uniqueness of mild solutions to stochastic partial functional integro-differential equations driven by a sub-fractional Brownian motion S Q H ⁢ ( t ) {S_{Q}^{H}(t)} , with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} . By the theory of resolvent operator developed by R. Grimmer (1982) to establish the existence of mild solutions, we give sufficient conditions ensuring the existence, uniqueness and the asymptotic behavior of the mild solutions. An example is provided to illustrate the theory.

Almost sure asymptotic stability for some stochastic partial functional integrodifferential equations on Hilbert spaces

AbstractIn this work, we study the asymptotic behavior of the mild solutions of a class of stochastic partial functional integrodifferential equation on Hilbert spaces. Using the stochastic convolution developed, we establish the exponential stability in p−mean square with p ≥ 2. Also, pathwise exponential stability is proved for p> 2. We extend the result of an example is provided for illustration.

Existence of Optimal Mild Solutions for Multi-valued Impulsive Stochastic Partial Functional Integrodifferential Equations

In this paper, we introduce a new class of multi-valued impulsive stochastic partial functional integrodifferential equations with infinite delay in the $$\alpha $$ -norm. Using stochastic analysis, analytic semigroup and fixed point strategy with the properties of fractional powers of closed operators, we establish the existence and uniqueness results of mild solutions for these equations with not instantaneous impulse. Then, the existence of optimal mild solutions is also proved. Particularly, the compactness of the operator semigroups is not needed. Finally, an example to illustrate the applications of main results is given.

Pseudo almost automorphic mild solution of nonautonomous stochastic functional integro-differential equations

In this paper, we propose a new class of stochastic process called (?,?)-pseudo almost automorphic in p-mean, which generalize in a natural fashion the concept of square-mean almost automorphy and its various extensions. As application, we establish the existence, uniqueness of(?,?)-pseudo almost automorphic in p-distribution mild solution to nonautonomous stochastic functional integro-differential equations. Finally, an example is given to illustrate the significance of the main findings.

Some results in stochastic functional integro-differential equations with infinite delays

In this paper, we study the results on averaging principle and stability of mild solutions for stochastic functional integro-differential equation with non-Lipschitz condition. We establish the result by the method of successive approximation and Bihari's inequality under the theory of resolvent operators. Finally, an example is provided for demonstration.

Some results in stochastic functional integro-differential equations with infinite delays

In this paper, we study the results on averaging principle and stability of mild solutions for stochastic functional integro-differential equation with non-Lipschitz condition. We establish the result by the method of successive approximation and Bihari's inequality under the theory of resolvent operators. Finally, an example is provided for demonstration.

Asymptotic behavior of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay

In this paper, the existence and asymptotic stability in p-th moment of mild solutions to a class of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay in Hilbert spaces is considered. By using H?lder?s inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdorff measure of noncompactness, a new set of sufficient conditions is formulated which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. These conditions do not require the nonlinear terms are assumed to be Lipschitz continuous. An example is also discussed to illustrate the efficiency of the obtained results.

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.