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2019 Topological characteristics of solution sets for fractional evolution equations and applications to control systems
Shouguo Zhu, Zhenbin Fan, Gang Li
Topol. Methods Nonlinear Anal. 54(1): 177-202 (2019). DOI: 10.12775/TMNA.2019.033

Abstract

This paper explores an abstract Riemann-Liouville fractional evolution model with a weighted delay initial condition. We develop the resolvent technique, a generalization of semigroup method, to formulate an appropriate notion of mild solutions to this abstract system and present the topological characteristics of the corresponding solution set in a weighted space. Furthermore, in view of the topological characteristics, we analyze the approximate controllability of the abstract system without Lipschitz assumption. We end up addressing an infinite dimensional fractional delay diffusion control system and a finite dimensional fractional ordinary differential control system by utilizing our theoretical findings.

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Shouguo Zhu. Zhenbin Fan. Gang Li. "Topological characteristics of solution sets for fractional evolution equations and applications to control systems." Topol. Methods Nonlinear Anal. 54 (1) 177 - 202, 2019. https://doi.org/10.12775/TMNA.2019.033

Information

Published: 2019
First available in Project Euclid: 8 July 2019

zbMATH: 07131279
MathSciNet: MR4018275
Digital Object Identifier: 10.12775/TMNA.2019.033

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 1 • 2019
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