Partial Neutral Integro-differential Equations Research Articles

On explicit abstract neutral differential equations with state-dependent delay

We introduce and study a class of abstract neutral differential equations with state-dependent delay at the temporal derivative. We study the local and global existence and uniqueness of mild solution and the existence of strict solution. Some examples concerning partial neutral integro-differential equations are presented.

Results on Neutral Partial Integrodifferential Equations Using Monch-Krasnosel’Skii Fixed Point Theorem with Nonlocal Conditions

In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel’skii type of fixed point theorem, a measure of noncompactness and resolvent operator theory. For this work, we have introduced some sufficient conditions to confirm the existence of the neutral partial integrodifferential system. An illustration of the derived results is offered at the end with a filter system corresponding to our existence result.

New Monch–Krasnosel’skii type fixed point theorems applied to solve neutral partial integrodifferential equations without compactness

In this paper, we show the existence of mild solutions for a class of neutral partial integrodifferential equations with lack of compactness. The results are obtained using noncompact resolvent operators and a new fixed point theorem of Monch-Krasnosel’skii type. Our results are applied to a large variety of partial differential equations in which memory effects are considered. An example is provided at the end of the paper to illustrate the main results of this work.

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.

Existence of an optimal control for fractional stochastic partial neutral integro-differential equations with infinite delay

Existence of an optimal control for fractional stochastic partial neutral integro-differential equations with infinite delay

On a new class of impulsive stochastic partial neutral integro-differential equations

In this paper, we introduce a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and not instantaneous impulses in separable Hilbert spaces. We prove the existence of mild solutions for these equations in the -norm without the assumptions of compactness. The results are obtained using suitable fixed point theorems with the properties of analytic resolvent operators. Finally, an example is presented to illustrate the theory.

EXISTENCE OF MILD SOLUTIONS OF PARTIAL NEUTRAL INTEGRODIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

We study the existence of mild solutions of partial neutral integrodifferential equations with unbounded delay by using the fixed point criterion for condensing operators.

Partial neutral functional integro-differential equations of fractional order with delay

Abstract In this paper we obtain sufficient conditions for the existence of solutions of some classes of partial neutral integro-differential equations of fractional order by using suitable fixed point theorems. MSC:26A33.

Existence of solutions for abstract neutral integro-differential equations with unbounded delay

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

Asymptotically almost periodic solutions for abstract neutral integro-differential equations

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered.

Asymptotically Almost Periodic Solutions for Abstract Partial Neutral Integro-Differential Equation

The existence of asymptotically almost periodic mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay is studied.

Existence results for a partial neutral integro-differential equation with state-dependent delay

Abstract. In this paper we study the existence of mild solutions for a class of abstractpartial neutral integro-differential equations with state-dependent delay. Keywords: Integro-differential equations, neutral equation, resolvent of operators, state-dependent delay.AMS-Subject Classification: 34K30, 35R10, 47D06.1. IntroductionIn this paper we study the existence of mild solutions for a class of abstract partialneutral integro-differential equations with state-dependent delay described in the formddt[x(t)+Z t−∞ N(t−s)x(s)ds] = Ax(t) +Z t−∞ (1.1) B(t− s)x(s)ds+f(t,x ρ(t,x t ) ),(1.2) x 0 = ϕ∈ B,where t∈ I= [0,b],A,B(t) for t≥ 0 are closed linear operators defined on a commondomain D(A) which is dense in X, N(t) (t≥ 0) is bounded linear operators on X, thehistory x t : (−∞,0] → Xgiven by x t (θ) = x(t+θ) belongs to some abstract phase spaceB defined axiomatically and f: [0,b]×B → Xand ρ: [0,b]×B → (−∞,b] are appropriatefunctions.Functional differential equations with state-dependent delay appear frequently in ap-plications as model of equations and for this reason the study of this type of equa-tions has received great attention in the last years. The literature devoted to thissubject is concerned fundamentally with first order functional differential equations forwhich the state belong to some finite dimensional space, see among another works,[1, 3, 4, 5, 7, 9, 10, 11, 12, 19, 21, 22]. The problem of the existence of solutions for partialfunctional differential equations with state-dependent delay has been recently treated inthe literature in [2, 14, 15, 16, 17]. Our purpose in this paper is to establish the exis-tence of mild solutions for the partial neutral system without using many of the strongrestrictions considered in the literature (see [6] for details).

Asymptotically Almost Periodic Solutions for Abstract Partial Neutral Integro-Differential Equation

Asymptotically Almost Periodic Solutions for Abstract Partial Neutral Integro-Differential Equation

Existence results for abstract partial neutral integro-differential equation with unbounded delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations

The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results.

Asymptotically Almost Periodic and Almost Periodic Solutions for Partial Neutral Integrodifferential Equations

Asymptotically Almost Periodic and Almost Periodic Solutions for Partial Neutral Integrodifferential Equations

Existence results for partial neutral integro-differential equation with unbounded delay

In this article, we study the existence and regularity of mild solution for a class of partial neutral integro-differential equation with unbounded delay.