EXISTENCE OF SOLUTIONS FOR FRACTIONAL EVOLUTION INCLUSION WITH APPLICATION TO MECHANICAL CONTACT PROBLEMS

Jinxia Cen (), Yongjian Liu, Nguyen van Thien () and Shengda Zeng
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Jinxia Cen: School of Science, Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu 610500, Sichuan, P. R. China
Yongjian Liu: Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, P. R. China
Nguyen van Thien: Department of Mathematics, FPT University, Education Zone, Hoa Lac High-Tech Park, Km29 Thang Long Highway, Thach That Ward, Hanoi, Vietnam
Shengda Zeng: Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, P. R. China4Faculty of Mathematics and Computer Science, Jagiellonian University in Krakow, ul. Lojasiewicza 6, 30348 Krakow, Poland

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-14

Abstract: The goal of this paper is to study an evolution inclusion problem with fractional derivative in the sense of Caputo, and Clarke’s subgradient. Using the temporally semi-discrete method based on the backward Euler difference scheme, we introduce a discrete approximation system of elliptic type corresponding to the fractional evolution inclusion problem. Then, we employ the surjectivity of multivalued pseudomonotone operators and discrete Gronwall’s inequality to prove the existence of solutions and its priori estimates for the discrete approximation system. Furthermore, through a limiting procedure for solutions of the discrete approximation system, an existence theorem for the fractional evolution inclusion problem is established. Finally, as an illustrative application, a complicated quasistatic viscoelastic contact problem with a generalized Kelvin–Voigt constitutive law with fractional relaxation term and friction effect is considered.

Keywords: Fractional Evolution Inclusion; Clarke Subgradient; Temporally Semi-Discrete Method; Pseudomonotone Operator; Quasistatic Viscoelastic Contact Problem (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400363

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