MIXED VARIATIONAL INEQUALITIES DRIVEN BY FRACTIONAL EVOLUTIONARY EQUATIONS

doi:10.1007/s10473-019-0211-9

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (2): 461-468.doi: 10.1007/s10473-019-0211-9

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MIXED VARIATIONAL INEQUALITIES DRIVEN BY FRACTIONAL EVOLUTIONARY EQUATIONS

Stanisłw MIGÓRSKI, Shengda ZENG

1. College of Sciences, Beibu Gulf University, Qinzhou 535000, China;Chair of Optimization and Control, Jagiellonian University in Krakow, ul. Lojasiewicza 6, 30348 Krakow, Poland;
2. Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, ul. Lojasiewicza 6, 30348 Krakow, Poland

Received:2018-01-26 Revised:2018-10-15 Online:2019-04-25 Published:2019-05-06
Contact: Shengda ZENG E-mail:zengshengda@163.com;shengdazeng@gmail.com;shdzeng@hotmail.com
Supported by:
This project has received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement (823731--CONMECH). It is supported by the National Science Center of Poland under Maestro Project (UMO-2012/06/A/ST1/00262), and National Science Center of Poland under Preludium Project (2017/25/N/ST1/00611). The first author is also supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland (3792/GGPJ/H2020/2017/0), Qinzhou University Project (2018KYQD06), and National Natural Sciences Foundation of Guangxi (2018JJA110006).

Abstract

Abstract: The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.

Key words: fractional differential variational inequality, C₀-semigroup, Minty mixed variational inequality, existence, mild solutions

Stanisłw MIGÓRSKI, Shengda ZENG. MIXED VARIATIONAL INEQUALITIES DRIVEN BY FRACTIONAL EVOLUTIONARY EQUATIONS[J].Acta mathematica scientia,Series B, 2019, 39(2): 461-468.

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MIXED VARIATIONAL INEQUALITIES DRIVEN BY FRACTIONAL EVOLUTIONARY EQUATIONS

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