Controllability of fractional measure evolution systems with state-dependent delay and nonlocal condition

IF 1.3 4区 数学 Q1 MATHEMATICS Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI:10.3934/eect.2022040
Yongyang Liu, Yansheng Liu
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引用次数: 1

Abstract

This paper is concerned with the existence of mild solutions and exact controllability for a class of fractional measure evolution systems with state-dependent delay and nonlocal conditions. We first establish an existence result of mild solutions for the concerned problem by applying an integral equation which is given in terms of probability density and semigroup theory. Then, the exact controllability are obtained by using the fractional calculus theory, Kuratowski measure of noncompactness and Mönch fixed point theorem, without imposing the Lipschitz continuity on nonlinear term. Finally, we give two applications to support the validity of the study.
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具有状态相关延迟和非局部条件的分数测度演化系统的可控性
研究一类具有状态依赖时滞和非局部条件的分数测度演化系统的温和解的存在性和精确可控性。首先利用概率密度和半群理论给出的一个积分方程,建立了该问题温和解的存在性结果。然后,利用分数阶微积分理论、Kuratowski非紧性测度和Mönch不动点定理,在不对非线性项施加Lipschitz连续性的情况下,获得了精确的可控性。最后,我们给出了两个应用来支持研究的有效性。
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来源期刊
Evolution Equations and Control Theory
Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.10
自引率
6.70%
发文量
5
期刊介绍: EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology
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