Neutral Functional Integrodifferential 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

New technique for solving the numerical computation of neutral fractional functional integro-differential equation based on the Legendre wavelet method

New technique for solving the numerical computation of neutral fractional functional integro-differential equation based on the Legendre wavelet method

Nondensely defined partial neutral functional integrodifferential equations with infinite delay under the light of integrated resolvent operators

Abstract In this work, we mainly focus on the local existence and regularity of integral solutions for a class of nondensely defined partial neutral functional integrodifferential equations with unbounded delay. We use the theory of integrated resolvent operators introduced by Oka [H. Oka, Integrated resolvent operators, J. Integral Equations Appl. 7 1995, 2, 193–232]. Finally, we provide an example to demonstrate the basic findings of our work.

Ulam–Hyers–Rassias Stability of Neutral Functional Integrodifferential Evolution Equations with Non-instantaneous Impulses on an Unbounded Interval

Ulam–Hyers–Rassias Stability of Neutral Functional Integrodifferential Evolution Equations with Non-instantaneous Impulses on an Unbounded Interval

Approximate Controllability of Neutral Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulses

In this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay. Our methodology relies on the utilization of resolvent operators in conjunction with Darbo’s fixed point theorem. To exemplify the practical implications of our findings, we provide an illustration.

New interpretation of topological degree method of Hilfer fractional neutral functional integro-differential equation with nonlocal condition

<abstract><p>This manuscript deals with the concept of Hilfer fractional neutral functional integro-differential equation with a nonlocal condition. The solution representation of a given system is obtained from the strongly continuous operator, linear operator and bounded operator, as well as the Wright type of function. The sufficient and necessary conditions for the existence of a solution are attained using the topological degree method. The uniqueness of the solution is attained by Gronwall's inequality. Finally, we employed some specific numerical computations to examine the effectiveness of the results.</p></abstract>

Existence and Asymptotic Periodicity of Solutions for Neutral Integro-Differential Evolution Equations with Infinite Delay

Abstract In this work, making use of the theory of resolvent operators and Banach fixed point theorem, we first discuss the existence and regularity of mild solutions for neutral partial functional integro-differential equations with infinite delay. We assume that the linear part of the considered equation generates a resolvent operator and the nonlinear function satisfies Lipschitz conditions. Then we investigate the asymptotic periodicity of mild solutions under asymptotic periodic assumption on the nonlinear function. The obtained results extend somewhat the related conclusions in literature. In the end, an example is presented to illustrate the obtained results.

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.

Sequential fractional order Neutral functional Integro differential equations on time scales with Caputo fractional operator over Banach spaces

<abstract><p>In this work, we scrutinize the existence and uniqueness of the solution to the Integro differential equations for the Caputo fractional derivative on the time scale. We derive the solution of the neutral fractional differential equations along the finite delay conditions. The fixed point theory is demonstrated, and the solution depends upon the fixed point theorems: Banach contraction principle, nonlinear alternative for Leray-Schauder type, and Krasnoselskii fixed point theorem.</p></abstract>

Global existence for neutral partial functional integrodifferential equations with infinite delay

The aim of this work is to prove some results about the existence and regularity of solutions for some neutral partial functional integrodifferential equations with infinite delay in Banach spaces. The results are based on semigroup theory and on Banach’s fixed point theorems. The method used treats the equations in its subspace D(A). One example is given to illustrate the theory.

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.

Existence results for ψ–Caputo fractional neutral functional integro-differential equations with finite delay

Existence results for ψ–Caputo fractional neutral functional integro-differential equations with finite delay

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 regularity of solutions for neutral partial integro-differential equations with nonlocal conditions

In this work, we study the existence of mild and classical solutions for neutral partial functional integro-differential equations with non-local condition. We discuss the problems by making full use of resolvent operators theory newly established in the literature, theory of fractional power, $$\alpha $$-norm and Schauder’s fixed point theorem. Some results on existence and regularity of solutions of the considered equation are obtained. Finally, an example is presented to illustrate the obtained results.

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 Regularity for Some Partial Neutral Functional Integrodifferential Equations with Nondense Domain

The paper is concerned with the study of some partial neutral functional integrodifferential equations with nondense domain. Using the integrated resolvent operator theory, we derive some results concerning the existence and regularity of solutions. Finally, an example is given to illustrate our theory.

Existence results for some neutral functional integrodifferential equations withbounded delay

In this paper, we study a class of neutral functional integrodifferential equations with finite delay in Banach spaces. We are interested in the global existence, uniqueness of mild solutions with values in the Banach space and in its subspace $D(A).$ The results are based on Banach's and Schauder's fixed point theorems and on the technique of equivalent norms. As an application, we consider a diffusion neutral functional integrodifferential equation.

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.