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Periodic mild solutions of impulsive fractional evolution equations

1 Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P. R. China
2 School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, P. R. China
3 Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynska doliná, 842 48 Bratislava, Slovakia, and Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia

Special Issues: Initial and Boundary Value Problems for Differential Equations

This paper studies the periodic mild solutions of impulsive fractional evolution equations. Firstly, the existence and stability of periodic solutions of impulsive fractional differential equations with varying lower limits for general impulses and small shifted impulses are considered. Secondly, the existence of periodic solutions of impulsive fractional differential equations with fixed lower limits is proved. Lastly, an example is given to demonstrate the result.
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© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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