Approximate controllability of second-order evolution differential inclusions in Hilbert spaces

In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of second-order evolution differential inclusions in Hilbert spaces. We use Bohnenblust-Karlin's fixed point theorem to prove our main results. Further, we extend the result to study the approximate controllability concept with nonlocal conditions and extend the result to study the approximate controllability for impulsive control systems with nonlocal conditions. An example is also given to illustrate our main results

Controllability of stochastic impulsive neutral functional differential equations driven by fractional Brownian motion with infinite delay

In this paper we study the controllability results of impulsive neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are obtained using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is provided to demonstrate the effectiveness of the theoretical result.Comment: 16 page

Controllability of Time-dependent Neutral Stochastic Functional Differential Equations Driven by a Fractional Brownian Motion

In this paper we consider the controllability of certain class of non-autonomous neutral evolution stochastic functional differential equations, with time varying delays, driven by a fractional Brownian motion in a separable real Hilbert space. Sufficient conditions for controllability are obtained by employing a fixed point approach. A practical example is provided to illustrate the viability of the abstract result of this work.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1401.2555, arXiv:1503.0798

Controllability of the impulsive semi linear beam equation with memory and delay

The semilinear beam equation with impulses, memory and delay is considered. We obtain the approximate controllability. 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.Comment: 10 page

Approximate controllability and optimal control of impulsive fractional semilinear delay differential equations with non-local conditions

In this paper we study the approximate controllability and existence of optimal control of impulsive fractional semilinear delay differential equations with non-local conditions. We use Sadovskii's fixed point theorem, semigroup theory of linear operators and direct method for minimizing a functional to establish our results. At the end we give an example to illustrate our analytical findings.Comment: 15 page

Controllability of the Strongly Damped Impulsive Semilinear Wave Equation with Memory and Delay

This article is devoted to study the interior approximated controllability of the strongly damped semilinear wave equation with memory, impulses and delay terms. The problem is challenging since the state equation contains memory and impulsive terms yielding to potential unbounded control sequences steering the system to a neighborhood of the final state, thus fixed point theorems cannot be used directly. As alternative, the A.E Bashirov and et al. techniques are applied and together with the delay allow the control solution to be directed to fixed curve in a short time interval and achieve our result

On Approximate Controllability of Impulsive Linear Evolution Equations

In this paper, we study an approximate controllability for the impulsive linear evolution equations in Hilbert spaces. The necessary and sufficient conditions for approximate controllability in terms of resolvent operators are given. An example is provided to illustrate the application of the obtained results

Partial-Approximate Controllability of Nonlocal Fractional Evolution Equations via Approximating Method

In this paper we study partial-approximate controllability of semilinear nonlocal fractional evolution equations in Hilbert spaces. By using fractional calculus, variational approach and approximating technique, we give the approximate problem of the control system and get the compactness of approximate solution set. Then new sufficient conditions for the partial-approximate controllability of the control system are obtained when the compactness conditions or Lipschitz conditions for the nonlocal function are not required. Finally, we apply our abstract results to the parial-approximate controllability of the semilinear heat equation and delay equation

Controllability of Neutral Stochastic Functional Integro-Differential Equations Driven by Fractional Brownian Motion with Hurst Parameter Lesser than 1/2

In this article we investigate the controllability for neutral stochastic functional integro-differential equations with finite delay, driven by a fractional Brownian motion with Hurst parameter lesser than $1/2$ in a Hilbert space. We employ the theory of resolvent operators combined with the Banach fixed point theorem to establish sufficient conditions to prove the desired resultComment: arXiv admin note: text overlap with arXiv:1503.07985 by other author

Controllability of fractional stochastic neutral functional differential equations driven by fractional Brownian motion with infinite delay

In this paper we study the controllability of fractional neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are obtained by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is provided to demonstrate the effectiveness of the theoretical result.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:1602.0580