Periodic mild solutions of impulsive fractional evolution equations

Lulu Ren; JinRong Wang; Michal Fečkan; Lulu Ren; JinRong Wang; Michal Fečkan

doi:10.3934/math.2020033

AIMS Mathematics

2020, Volume 5, Issue 1: 497-506. doi: 10.3934/math.2020033

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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

Received: 30 September 2019 Accepted: 19 November 2019 Published: 06 December 2019
MSC : 34A08, 34A37, 34C25

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.
- impulsive fractional differential equations,
- periodic mild solution,
- existence,
- stability
Citation: Lulu Ren, JinRong Wang, Michal Fečkan. Periodic mild solutions of impulsive fractional evolution equations[J]. AIMS Mathematics, 2020, 5(1): 497-506. doi: 10.3934/math.2020033

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Abstract

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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