Open AccessComplete controllability for a class of fractional evolution equations with uncertainty
Author(s) -
Nguyen Thi Kim Son,
Nguyen Phuong Dong,
Lê Hoàng Sơn,
A. Khastan,
Hoàng Việt Long
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020104
Subject(s) - controllability , mathematics , compact space , semigroup , subspace topology , metric space , fixed point theorem , fuzzy logic , hausdorff space , class (philosophy) , hausdorff distance , pure mathematics , discrete mathematics , mathematical analysis , computer science , artificial intelligence
In this paper, we study the complete controllability for a class of fractional evolution equations with a common type of fuzzy uncertainty. By using Hausdorff measure of noncompactness and Krasnoselskii's fixed point theorem in complete semilinear metric space, we give some sufficient conditions of the controllability for the fuzzy fractional evolution equations without involving the compactness of strongly continuous semigroup and the perturbation function. In addition, the controllable problem is considered in a subspace of fuzzy numbers in which the gH-differences always exist, that guarantees the satisfaction of hypotheses of the problem. An application example related to electrical circuit is given to illustrate the effectiveness of theoretical results.