Neutral Functional Integrodifferential Inclusions Research Articles

Controllability results for Sobolev-type analytic resolvent nonlocal neutral functional integrodifferential inclusions with impulses

This article aims to explore the existence and controllability strategies for Sobolev-type nonlocal neutral functional integrodifferential inclusions with impulses via the resolvent operator. Initially, the article is divided into two main parts. The first part is dedicated to establishing the existence of mild solutions for the given system and introducing a new set of sufficient conditions for approximate controllability. These findings are derived under the assumption that the corresponding linear system is approximately controllable. The second part builds on these results by establishing the existence of an optimal control pair for the Lagrange problem (P) based on an appropriate set of sufficient conditions. The development of these results heavily relies on Bohnenblust–Karlin's fixed-point method, semigroup theory, multivalued analysis, and the resolvent operator. Finally, an example is provided to clarify the concepts discussed.

Approximate Controllability of a Neutral Stochastic Fractional Integro-Differential Inclusion with Nonlocal Conditions

This paper discusses the approximate controllability of a neutral functional integro-differential inclusion involving Caputo fractional derivative in a Hilbert space under the assumptions that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of neutral fractional stochastic functional integro-differential inclusions are formulated and established by utilizing stochastic analysis theory, fractional calculus and the technique of fixed point theorem with analytic compact resolvent operator. An example is also considered for illustrating the discussed theory.

English

In this paper, we prove the sufficient condition for the controllability of second order impulsive neutral functional integrodifferential inclusions with an infinite delay in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families and fixed point theorem for condensing maps due to Martelli.

Impulsive Problems for Fractional Partial Neutral Functional Integro-Differential Inclusions with Infinite Delay and Analytic Resolvent Operators

In this paper, the existence of mild solutions for a class of impulsive fractional partial neutral functional integro-differential inclusions with infinite delay and analytic α-resolvent operators in Banach spaces is investigated. Sufficient conditions for the existence are derived with the help of the fixed-point theorem for discontinuous multi-valued operators due to Dhage and the fractional power of operators combined with approximation techniques. An example is provided to illustrate the theory.

Existence Results for a Second Order Impulsive Neutral Functional Integrodierential Inclusions in Banach Spaces with Innite Delay

A fixed point theorem for condensing maps due to Martelli combined with theories of a strongly continuous cosine family of bounded linear operators is used to investigate the existence of solutions to second order impulsive neutral functional integrodifferential inclusions with infinite delay in Banach spaces.

Controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay

In this paper, a sufficient condition is established for the controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay in Banach spaces. The approach used is analytic semigroups and fractional powers of closed operators and nonlinear alternative of Leray–Schauder type for multivalued maps due to D. O'Regan.

Existence results of impulsive partial neutral integrodifferential inclusions with infinity delay

This paper investigates a class of impulsive partial neutral functional integrodifferential inclusions with infinite delay in Banach spaces. The existence of mild solutions of these inclusions is determined under the mixed Lipschitz and Carathéodory conditions by using another nonlinear alternative of Leray–Schauder type for multivalued maps due to D. O’Regan.

Existence results of second-order impulsive neutral functional integrodifferential inclusions with unbounded delay in Banach spaces

This paper investigates a class of second-order impulsive neutral functional integrodifferential inclusions with unbounded delay in Banach spaces. The existence of mild solutions of these inclusions is determined by using the theory of cosine families of bounded linear operators and a recent fixed point theorem for multivalued maps due to Dhage.

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators.

Existence results for functional and neutral functional integrodifferential inclusions with lower semicontinuous right-hand side

In this paper, Schaefer's fixed point theorem combined with a selection theorem due to Bressan and Colombo is used to investigate the existence of solutions for the first- and second-order functional and neutral functional integrodifferential inclusions with lower semicontinuous and nonconvex-valued right-hand side.