Topological structure of solution set for a class of fractional neutral evolution equations on the half-line

Le Hoan Hoa, Nguyen Ngoc Trong, Le Xuan Truong

DOI: http://dx.doi.org/10.12775/TMNA.2016.044

Abstract


A topological structure of the set of all mild solutions of fractional neutral evolution equations with finite delay on the half-line is investigated. We show that the solution set is an R$_\delta$-set. It is proved on compact intervals by establishing a result on topological structure of fixed point set of Krasnosel'skiĭ type operators. Next, using the inverse limit method, we obtain the same result on the half-line.

Keywords


Topology structure; solution set; fractional differential equation; Krasnosel'skiĭ type operator

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