Partial Functional Integrodifferential Equations Research Articles

Approximate Controllability of a Coupled Nonlocal Partial Functional Integro-differential Equations with Impulsive Effects

Approximate Controllability of a Coupled Nonlocal Partial Functional Integro-differential Equations with Impulsive Effects

Existence results, regularity and compactness properties, in the $$\alpha $$-norm, for semilinear partial functional integrodifferential equations with nonlinear Kernel and delay argument

Existence results, regularity and compactness properties, in the $$\alpha $$-norm, for semilinear partial functional integrodifferential equations with nonlinear Kernel and delay argument

Controllability result in α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces

Abstract The purpose of this paper is to study the controllability in the α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach space. To do this, we give sufficient conditions ensuring the controllability by assuming that the undelayed part admits a resolvent operator in the sense of Grimmer and that the delayed part is continuous with respect to the fractional power of the generator. The results are obtained by using the Schauder fixed-point theorem.

On the existence of mild solutions of some partial functional integrodifferential equations with non continuous state-dependent delay function

On the existence of mild solutions of some partial functional integrodifferential equations with non continuous state-dependent delay function

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.

Results on existence of solutions in nonlocal partial functional integrodifferential equations with finite delay in nondense domain

In this work, to show the existence and uniqueness solution of functional integrodifferential equation with nonlocal condition and finite delay function. This article contains continuously dependence of integral solution and existence of strict solution established by using integrated resolvent operator theory with support of Lipschitz continuous. In this article the operator (T(t))t⩾0 is assumed the locally Lipschitz continuous integrated resolvent operator and proved the existence of strict solution on reflexive and general Banach spaces. Finally an example is given related to this work.

On the approximate boundary controllability of some partial functional integrodifferential equations with finite delay in Banach spaces

<p style='text-indent:20px;'>This work concerns the study of approximate boundary controllability for some nonlinear partial functional integrodifferential equations with finite delay arising in the modeling of materials with memory, in the framework of general Banach spaces. We give sufficient conditions that ensure the approximate controllability of the system by supposing that its linear undelayed part is approximately controllable, admits a resolvent operator in the sense of Grimmer, and by making use of the Banach fixed-point Theorem and the continuity of the resolvent operator in the uniform norm-topology. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator and the uniform boundedness of the nonlinear term. An example of applications is given for illustration.</p>

Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces

Abstract In this work, we discuss the approximate controllability of some nonlinear partial functional integrodifferential equations with nonlocal initial condition in Hilbert spaces. We assume that the corresponding linear part is approximately controllable. The results are obtained by using fractional power theory and α-norm, the measure of noncompactness and the Mönch fixed-point theorem, and the theory of analytic resolvent operators for integral equations. As a result, we obtain a generalization of the work of Mahmudov [N. I. Mahmudov, Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Anal. 68 2008, 3, 536–546], without assuming the compactness of the resolvent operator. Our results extend and complement many other important results in the literature. Finally, a concrete example is given to illustrate the application of the main results.

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.

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.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

Existence and regularity of solutions in $$\alpha $$-norm for some partial functional integrodifferential equations in banach spaces

In this work, we study the existence and regularity of solutions in $$\alpha $$ -norm for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator, the delayed part is assumed to be locally lipschitz. Firstly, we show the existence of mild solutions. Secondly, we give sufficiently conditions ensuring the existence of strict solutions.

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 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.

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.

Global existence for some neutral functional integrodifferential equations with finite delay

In this paper, we study a class of neutral partial functional integrodifferential equations with finite delay in Banach spaces. We are interested in the global existence, uniqueness and regularity of solutions with values in the subspace $D(A).$ The method used are based on Banach's fixed point theorem and on the technique of the graph norm. In our work the nonlinear term is treated as a perturbation of the linear equation. As an application, we consider a diffusive neutral partial functional integrodifferential equation.

Solvability of nondensely defined partial functional integrodifferential equations using the integrated resolvent operators

Solvability of nondensely defined partial functional integrodifferential equations using the integrated resolvent operators

Approximate Controllability Results for Impulsive Partial Functional Nonlocal Integro-differential Evolution Systems through Resolvent Operators

This paper investigates the existence and approximate controllability results for a class of impulsive functional integro-differential evolution systems with nonlocal conditions via resolvent operators in Banach spaces. By making utilization of Banach contraction principle and Schaefer’s fixed point theorem along with resolvent operators and semigroup theory, we build up the desired results. As an application, we also consider an impulsive partial functional integro-differential equations.

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.