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This paper deals with the control problems governed by fractional impulsive functional evolution equations with state-dependent delay involving Caputo fractional derivatives in Banach spaces. The main objective of this work is to formulate sufficient conditions for the approximate controllability of the considered system in separable reflexive Banach spaces. We have exploited the resolvent operator technique and Schauder's fixed point theorem in the proofs to achieve this goal. The approximate controllability of linear system is discussed in detail, which lacks in the existing literature. Moreover, we point out some shortcomings of the existing works in the context of characterization of mild solution, phase space, and approximate controllability of fractional order impulsive systems in Banach spaces. Finally, we investigate the approximate controllability of the fractional order heat equation with non-instantaneous impulses and delay by using the developed results. [ABSTRACT FROM AUTHOR]

This article is concerned with the approximate controllability for some fractional evolution inclusions of Sobolev and Clarke subdifferential type, which can be used to study fractional hemivariational inequalities. Using two characteristic solution operators and their fundamental properties via a fixed point theorem for multi-valued maps, we derive sufficient conditions for approximate controllability of linear and semi-linear controlled systems. Finally, two examples are given to illustrate our theory. [ABSTRACT FROM AUTHOR]

The semilinear beam equation with impulses, memory and delay is considered and its approximate controllability obtained. This is done by employing a technique that avoids fixed point theorems and pulling back the control solution to a fixed curve in a short time interval. Demonstrating, once again, that the controllability of a system is robust under the influence of impulses and delays. [ABSTRACT FROM AUTHOR]

This article is mainly concerned with the study of controllability for a class of second order control problems in Hilbert spaces, for which the uniqueness is not available. We show the approximate controllability of the non-linear problem via that of its corresponding linear problem by using the fixed point theory for multivalued maps with non-convex values. We also obtain some results on the continuity of solution map and the topological structure of the solution set of the problem at hand. Finally, an example is given for the demonstration of the theory obtained. [ABSTRACT FROM AUTHOR]

In this work, we study the approximate controllability for a class of semilinear stochastic evolution systems with finite delays in |$L_p$| space. The main technique is the fundamental solution theory constructed through Laplace transformation. The approximate controllability result is obtained via the so-called resolvent condition. The nonlinear terms are only required to be partly uniformly bounded. An example is provided to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this article, by the semi-group theory, fractional calculus, stochastic analysis theory and the fixed-point technique, we provide sufficient conditions for the existence of mild solutions and the approximate controllability of Caputo fractional neutral stochastic differential inclusions with state-dependent delay (under the assumption that the corresponding linear system is approximately controllable). An example is provided to illustrate the abstract results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present some sufficient conditions for approximate and exact controllability of semilinear stochastic control system with finite delay. Sufficient conditions for approximate controllability are obtained by separating the given semilinear system into two systems namely a semilinear deterministic system and a linear stochastic system using Schauder fixed point theorem. For obtaining the sufficient conditions for exact controllability of assumed system, Banach fixed point theorem is applied. Instead of a C0-semigroup associated with the mild solution of the system we use the so-called fundamental solution. At the end, examples are given to illustrate the theory. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of abstract neutral integro-differential inclusions with infinite delay in Hilbert spaces. We establishes a set of sufficient conditions for the approximate controllability for a class of abstract neutral integro-differential inclusions with infinite delay in Hilbert spaces by using Bohnenblust-Karlin's fixed point theorem. An example is also given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this article we establish sufficient conditions for the approximate controllability of retarded semilinear integrodifferential control systems with unbounded operators under simple conditions on the controller and a weak backward uniqueness property for the adjoint system of the corresponding linear system. A simple example to which our main result can be applied is given. [ABSTRACT FROM AUTHOR]

In this article, the problem of approximate controllability for impulsive fractional stochastic partial neutral integrodifferential inclusions with infinite delay in a Hilbert space is investigated. By using the Hölder inequality, the analytic α-resolvent operator and fixed point strategy with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of an impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an illustrative example is given to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the approximate controllability of fractional stochastic integrodifferential equations with infinite delay of order 1

The main purpose of this paper is studying the approximate controllability for boundary control systems when the controls take values in a convex cone of the control space. Characterization for approximate controllability is given. Necessary and sufficient conditions are formulated and proved. The abstract results are illustrated by studying the approximate boundary controllability for a linearized Saint-Venant equation and the heat equation where the control is positive. [ABSTRACT FROM AUTHOR]

In this paper, applying the Rothe's Fixed Point Theorem, we prove the approximate controllability of the following semilinear Beam equation: ... in the states space Z1 = D(-Δ) × L2(O) endowed with the graph norm, whereβ >1, O is a sufficiently regular bounded domain in RN, the distributed control u belongs to L2([0, t ];U) (U = L2(O)) and the non-linear function f : [0, t ] × R × R × R -→ R is smooth enough and there are η, b, c ∈ R with 1/2 ≤ η ≤ 1 such that We prove that for all t >0 this system is approximately controllable on [0, t ]. [ABSTRACT FROM AUTHOR]

This paper considers the approximate controllability for a class of neutral control systems governed by semilinear neutral delayed equations. Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using Banach fixed-point principle. The obtained results improve some existing analogous ones to some extent. An example is presented to illustrate the applications of the obtained results. [ABSTRACT FROM PUBLISHER]

Recently, the problem of approximate controllability has been extensively studied by many authors. However, up to now approximate controllability problems for fractional functional evolution inclusions with delay have not been considered in the literature. To fill this gap, this paper investigate the approximate controllability problem for fractional functional evolution inclusions in Hilbert spaces. The results are obtained under the corresponding linear system is approximately controllable. By using the fixed-point theorem for condensing multivalued maps and semigroup theory, sufficient conditions are formulated and proved. In the end, we give two examples to illustrate the application of the abstract results. [ABSTRACT FROM PUBLISHER]

In this paper, we prove the approximate controllability of control systems governed by a class of partial fractional neutral integro-differential inclusions with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the fixed-point theorem for discontinuous multi-valued operators due to Dhage with the α-resolvent operator. An example is provided to illustrate the main results. [ABSTRACT FROM PUBLISHER]

We study the approximate controllability of the stochastic Maxwell equations with an abstract approach and a constructive approach using a generalization of the Hilbert uniqueness method as proposed in Kim (2004, Approximate controllability of a stochastic wave equation. Appl. Math. Optim., 49, 81–98) for the stochastic wave equation. [ABSTRACT FROM PUBLISHER]

In this paper, semi-linear retarded stochastic control systems together with conditions for approximate controllability of associated linear system is used to obtain sufficient conditions for approximate controllability results in Hilbert spaces. An example is also provided to illustrate the theory. [ABSTRACT FROM PUBLISHER]

In this paper, we present necessary and sufficient conditions for the exact and approximate controllability of the following linear difference equation:where Z, U are Hilbert spaces, A(·) ∈ l∞(, L(Z)), B(·) ∈ l∞(, L(U, Z)), u ∈ l2(, U) and * = ∪ {0}. Moreover, in the case of exact controllability, the control u ∈ l2(, U) steering an initial state z0 to a final state z1 in time n0 is given by the formula according to Lemma 2.1. As a particular case, we consider the discretization on flow of the following controlled evolution equation z′ = Az + Bu, z ∈ Z, u ∈ U, t > 0, where B ∈ L (U, Z), u ∈ L2(0, τ;U) and A is the infinitesimal generator of a strongly continuous semigroup {T(t)}t ≥ 0 in Z, given byaccording to Lemma 1.1. These results are applicable to a broad class of reaction–diffusion systems such as the heat equation, the wave equation, the equation modelling the damped flexible beam, the strongly damped wave equation, the thermoelastic plate equation, etc. In Section 4, these results are applied to a discrete version of the n-dimensional heat and n-dimensional wave equation. [ABSTRACT FROM PUBLISHER]

In this paper, the approximate controllability of non-linear evolution time-varying delay systems with preassigned responses is studied. These controllability results are for non-linear systems that are not associated with linear systems and no compactness assumption is imposed. [ABSTRACT FROM PUBLISHER]

In this paper we study the controllability of the following controlled Ornstein–Uhlenbeck equation [ABSTRACT FROM PUBLISHER]

In this paper we give a necessary and sufficient algebraic condition for the approximate controllability of the following thermoelastic plate equation with Dirichlet boundary conditions [ABSTRACT FROM PUBLISHER]

The Nussbaum fixed‐point theorem together with conditions for approximate controllability of linear systems are used to obtain sufficient conditions for approximate controllability of associated semilinear stochastic systems in Hilbert spaces. [ABSTRACT FROM PUBLISHER]