Topological characteristics of solution sets for fractional evolution equations and applications to control systems

Shouguo Zhu, Zhenbin Fan, Gang Li



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.


Fractional diffusion control system; approximate controllability; resolvent; $R_{\delta}$-set

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