Neutral Integrodifferential Systems Research Articles

On the fractional perturbed neutral integro-differential systems via deformable derivatives: an existence study

In this paper, we provide some appropriate conditions for the existence of solutions for a perturbed fractional neutral integro-differential system under the deformable derivative in a Banach space. Using the Banach contraction principle and Krasnoselskii’s fixed point theorem, we establish some new existence theorems. Moreover, we provide two numerical examples to demonstrate the applicability of the theoretical results

ON THE INITIAL VALUE PROBLEMS FOR NEUTRAL INTEGRO-DIFFERENTIAL SYSTEM WITHIN EXPONENTIAL KERNEL

This paper deals with the existence results for neutral integro-differential system (NIDS) through Caputo-Fabrizio (CF) operator. The solution to our addressing system, which can be considered innovative, is explained and proven in preliminary section. Certain novel existence findings are shown using fixed point approaches. Finally, two numerical examples are provided in the work to demonstrate the application of our theoretical findings.

Boundary Controllability of Semilinear Impulsive Sobolev-type Neutral Integrodifferential System with Timevarying Delays in Banach Space

Boundary Controllability of Semilinear Impulsive Sobolev-type Neutral Integrodifferential System with Timevarying Delays in Banach Space

An exploration of controllability on Hilfer fractional system via integral contractor

The primary focus of this article is to provide sufficient conditions for the controllability of Hilfer fractional neutral integrodifferential systems. By using the theories on fractional calculus, semigroup theory, and fixed point theorem method, the results are proved through integral contractors for the nonlinear neutral evolution equation in a non‐dense domain. In the end, the derived outcomes are validated through suitable illustrations.

Approximate controllability of Atangana-Baleanu fractional neutral delay integrodifferential stochastic systems with nonlocal conditions☆

The study of approximate controllability results ensures the essential conditions required for a solution. Keeping the importance of the study, we initiate the existence and approximate controllability an Atangana-Baleanu-Caputo (ABC)-fractional order neutral delay integrodifferential stochastic systems with nonlocal conditions. For this purpose, the suggested ABC-fractional order neutral integrodifferential stochastic system is transferred into an equivalent fixed point problem via an integral operator. The operator is then analyzed for boundedness, continuity and equicontinuity. Then Arzela-Ascolli theorem ensures the compact multivalued function of the operator and Martelli’s fixed point theorem is utilized for the existence of the mild solution. Based on the fixed point theorem and Dunford-Pettis theorem joined with ζ -resolvent operators, we develop the approximate controllability results. Finally, an example is given to justify the theoretical results. The achieved results reveal that the proposed method is systematic and suitable for dealing with the stochastic fractional problems arising in physics, technology, and engineering in terms of the ABC fractional derivative.

Optimal feedback control problems for a semi-linear neutral retarded integro-differential system

This article considers the optimal and time optimal feedback control problems for a semi-linear neutral retarded integro-differential system. The existence of mild solutions and feasible pairs for the considered system is studied by applying theory of resolvent operators for linear neutral integro-differential evolution systems, fractional powers of operators and Schauder fixed point theorem. Then the Lagrange optimal feedback control problem for the system is investigated via limit arguments under some suitable assumptions. The time optimal feedback control problem is proposed and discussed deliberately here as well. An example is presented in the end to illustrate the obtained results.

On fractional state-dependent delay integro-differential systems under the Mittag-Leffler kernel in Banach space

<abstract><p>The existence of Atangana-Baleanu fractional-order semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces is investigated in this paper. We establish the existence findings by using Monch's fixed point theorem and the concept of measures of non-compactness. A functioning example is provided at the end in order to illustrate the findings reached from the theoretical study.</p></abstract>

Discussion on boundary controllability of nonlocal fractional neutral integrodifferential evolution systems

<abstract><p>In the present work, we have established sufficient conditions for boundary controllability of nonlocal fractional neutral integrodifferential evolution systems with time-varying delays in Banach space. The outcomes are obtained by applying the fractional theory and Banach fixed point theorem. At last, we give an application for the validation of the theoretical results.</p></abstract>

Null boundary controllability of nonlinear integrodifferential systems with Rosenblatt process

By using stochastic analysis, compact semigroups and Schauder fixed-point theorem, we discuss the null boundary controllability of nonlinear integrodifferential system with Rosenblatt process. In addition, the null boundary controllability of Sobolev-type neutral integro-differential system with Rosenblatt is studied. Finally, an example is given to illustrate the obtained results. The null controllability results for stochastic differential systems with Rosenblatt process and control on the boundary have not yet been considered in the literature, and this fact motivates this work.

Existence results for Atangana-Baleanu fractional neutral integro-differential systems with infinite delay through sectorial operators

This manuscript’s main objective is to examine the existence of mild solution of Atangana-Baleanu fractional order semi-linear integro-differential equations [ABFSIDE] and semi-linear neutral integro-differential evolution equations [ABFSNIDE] with infinite delay [ID] in Banach spaces. We introduce an appropriate definition of a mild solution for these systems. Based on the Banach contraction principle, nonlinear alternative of Leray-Schauder type and Krasnoselskii-Schaefer fixed point theorem joined with ρ-resolvent operators, we develop the main results. Finally, an example is given to justify the theoretical results.

Optimal control problems for a neutral integro-differential system with infinite delay

<p style='text-indent:20px;'>This work devotes to the study on problems of optimal control and time optimal control for a neutral integro-differential evolution system with infinite delay. The main technique is the theory of resolvent operators for linear neutral integro-differential evolution systems constructed recently in literature. We first establish the existence and uniqueness of mild solutions and discuss the compactness of the solution operator for the considered control system. Then, we investigate the existence of optimal controls for the both cases of bounded and unbounded admissible control sets under some assumptions. Meanwhile, the existence of time optimal control to a target set is also considered and obtained by limit arguments. An example is given at last to illustrate the applications of the obtained results.</p>

Approximate controllability for finite delay nonlocal neutral integro-differential equations using resolvent operator theory

In this paper, our purpose is to study the approximate controllability of abstract nonlocal neutral integro-differential equations with finite delay in a Hilbert space using the resolvent operator theory. We derive a variation of parameters formula for representing a solution of the given neutral integro-differential system in the form of resolvent operators and then define a mild solution of the system. We also study the existence of a mild solution of the system with the help of resolvent operator theory. The fractional power theory, $$\alpha $$ -norm, resolvent operator theory, semigroup theory and Krasnoselskii’s fixed point theorem are used to prove the approximate controllability of the system. Finally, we illustrate our results with the help of an example.

On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions

Abstract In this article, we study an impulsive neutral fractional integro-differential equation (FIDE) via Atangana-Baleanu fractional derivative. The fixed point approach is employed to prove the existence results of the equation with initial and non-local conditions. The application of the results obtained are verified using suitable examples of different fractional orders.

Existence of Second Order Impulsive Neutral Integro-Differential Evolution Control Systems with an Infinite Delay

This article, we study sufficient conditions for the controllability of second-order impulsive neutral integro-differential evolution systems with an infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

Existence results for a class of impulsive neutral fractional stochastic integro-differential systems with state dependent delay

In this paper, we provide a framework for study the mild solution to fractional neutral stochastic integro-differential systems with state dependent delay and noninstantaneous impulses in Hilbert spaces. To obtain the existence results, we have utilized the concepts of fractional calculus, fixed point theorems, stochastic analysis and semigroup theory. Finally, examples are provided to demonstrate the obtained results.

Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators

Abstract The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces. Based on the Banach contraction principle and Krasnoselskii fixed point theorem (FPT) joined with resolvent operators, we develop the main results. Ultimately, an representation is also offered to demonstrate the accomplished theorem.

New results on exact controllability of a class of fractional neutral integro-differential systems with state-dependent delay in Banach spaces

This article deals with the use of Krasnoselskii’s fixed point theorem and Leray–Schauder alternative theorem combined with resolvent operator and some analytical methods to investigate the exact controllability and continuous dependence of a class of neutral fractional integro-differential systems with state-dependent delay in Banach spaces. An application to exemplify the concept is provided at the end.

Local existence for an impulsive fractional neutral integro-differential system with Riemann\u2013Liouville fractional derivatives in a Banach space

In this manuscript, we investigate a sort of fractional neutral integro-differential equations with impulsive outcomes and extend the formula of general solutions for the impulsive fractional neutral integro-differential system in a Banach space. By using the analysis of the limit case and the operator generating compact semigroup, we derive the main results. Finally, an example is discussed to illustrate the efficiency of the results.

Results on Existence and Uniqueness of Solution Of Impulsive Neutral Integro-Differential System

In this work, the solution of the impulsive neutral integro-differential system is analysed. The Du Bois–Reymond’s assumptions on solution variation of piecewise smooth functions are used to establish the existence of only the impulsive term as a solution of the system at the points of discontinuity. The theories of infinitesimal generator of a strongly continuous compact semigroup is used to formulate theorems on existence and uniqueness of system solution, and proves are provided using an approximate piecewise continuous, compact operator and a continuous positive non decreasing function . Results obtained are improvement on the qualitative analysis of impulsive neutral integro-differential system

On fractional neutral integro-differential systems with state-dependent delay via Kuratowski measure of non-compactness in Banach spaces

On fractional neutral integro-differential systems with state-dependent delay via Kuratowski measure of non-compactness in Banach spaces