Abstract:We establish the existence of mild solutions and periodic mild solutions for a class of abstract rst-order non-autonomous neutral functional differential equations with innite delay in a Banach space.
“…where A is infinitesimal generator of a strongly continuous semigroup. Herniquez and Vasquez [13] proved the existence of almost periodic solution to (2.5). These types of equations are often referred to as the abstract retarded functional differential equation.…”
In this article, we prove sufficient conditions for the existence of almost periodic solutions to a non-instantaneous impulsive differential equation with deviating argument. The results are established with the help of fixed point theorem. We also show that the solution is asymptotically stable. We conclude the article with an example to illustrate the main results.
“…where A is infinitesimal generator of a strongly continuous semigroup. Herniquez and Vasquez [13] proved the existence of almost periodic solution to (2.5). These types of equations are often referred to as the abstract retarded functional differential equation.…”
In this article, we prove sufficient conditions for the existence of almost periodic solutions to a non-instantaneous impulsive differential equation with deviating argument. The results are established with the help of fixed point theorem. We also show that the solution is asymptotically stable. We conclude the article with an example to illustrate the main results.
“…Akdad et al 35 presented existence results for the Stepanov 𝜇-pseudo almost automorphic and periodic mild solution. Zhou and Jiao, Vijayakumar and Udhayakumar, Hernández and O'Regan, and Henriquez [36][37][38][39] investigated existence and uniqueness for certain classes of the fractional system by employing the fixed point approach, fractional theories, and measure of noncompactness, etc.…”
Sufficient conditions for boundary controllability of nonlocal impulsive neutral integrodifferential evolution equations are explored. In the first problem, the outcomes are proven with the help of Sadovskii's fixed point theorem collaborated with strongly continuous semigroup theory. In the second problem, we considered nonautonomous evolution equations, and the result is proven by employing Sadovskii's fixed point theorem in collaboration with the evolution system. Examples are included to demonstrate the theoretical results for both types of equations.
“…See [9,10] for a more practical background of this kind of equations. In the past years, existence results and asymptotic properties of solutions for this type of neutral systems have been investigated by many authors (e.g., [11][12][13][14][15][16][17]).…”
In this work, we study the approximate controllability for a class of neutral control systems governed by semi-linear neutral equations with infinite delay in Hilbert space. Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using resolvent condition and techniques of fractional power operators. An example is also provided to illustrate the applications of the obtained results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.