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Structure of the Solution Set to Fractional Differential Inclusions with Impulses at Variable Times on Compact Interval

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Abstract

A topological structure of the solution set to a class of fractional differential inclusions with (or impulses at variable times) is investigated. It is shown that the solution set is an \(R_{\delta }\)-set under some assumptions by the well-known theorem Bothe, D.: Multivalued perturbations of m-accretive differential inclusions. Israel J. Math. 108, 109–138 (1998) and the generalized Gronwall inequality under suitable Banach space. One example is listed for illustrating the main results.

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Acknowledgements

This research was supported by the Natural Science Foundation Project of Universities in Anhui Province(KJ2018A0027). The authors are extremely grateful to the reviewers for their valuable comments and suggestions, which have contributed much to the improved presentation of this paper.

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Qi Wang & Xiaoyue Li

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  1. Qi Wang
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  2. Xiaoyue Li
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Wang, Q., Li, X. Structure of the Solution Set to Fractional Differential Inclusions with Impulses at Variable Times on Compact Interval. Qual. Theory Dyn. Syst. 20, 59 (2021). https://doi.org/10.1007/s12346-021-00500-x

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