Related papers: Controllability problem of an evolution equation w…
The current study addresses the control problems posed by a semilinear neutral integro-differential equation with memory. The primary objectives of this study are to investigate the existence of a mild solution and approximate…
This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the…
In this work we extend a variational method to study the approximate controllability and finite dimensional exact controllability ( finite-approximate controllability) for the semilinear evolution equations in Hilbert spaces. We state a…
A study of the linear quadratic (LQ) control problem on a finite time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop…
In this paper we consider the heat equation with memory in a bounded region $\Omega \subset\mathbb{R}^d$, $d\geq 1$, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of…
In this paper, we consider a non-autonomous nonlinear evolution equation in separable, reflexive Banach spaces. First, we consider a linear problem and establish the approximate controllability results by finding a feedback control with the…
This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability…
In this article we study the optimal control problem with quadratic functionals for a linear Volterra integro-differential equation in Hilbert spaces. With the finite history seen as an (additional) initial datum for the evolution,…
This paper investigates the controllability of systems governed by conformable fractional order derivatives. It first establishes the existence and uniqueness of evolution operators for non-autonomous fractional-order homogeneous systems,…
We study the existence of mild solutions and the approximate controllability for nonautonomous integrodifferential equations with state-dependent delay. We assume the approximate controllability of the linear part, and then we use resolvent…
A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer…
We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…
Inspired in our work on the controllability for the semilinear with memory \cite{Carrasco-Guevara-Leiva:2017aa, Guevara-Leiva:2016aa, Guevara-Leiva:2017aa}, we present the general cases for the approximate controllability of impulsive…
We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on…
This article is devoted to the study of null controllability for evolution equations that incorporate both memory and delay effects. The problem is particularly challenging due to the presence of memory integrals and delayed states, which…
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…
In this paper we study the approximate controllability of fractional partial differential equations associated with the so-called Hilfer type time fractional derivative and a non-negative selfadjoint operator $A$ with a compact resolvent on…
We study a general class of control systems with memory, which in particular includes systems with fractional derivatives and integrals and also the standard heat equation. We prove that the approximate controllability property of the heat…
The current article examines the approximate controllability problem for non-instantaneous impulsive fractional evolution equations of order $1<\alpha<2$ with state-dependent delay in separable reflexive Banach spaces. In order to establish…
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…