Articles

THE NONEMPTINESS AND COMPACTNESS OF MILD SOLUTION SETS FOR RIEMANN-LIOUVILLE FRACTIONAL DELAY DIFFERENTIAL VARIATIONAL INEQUALITIES

  • Yirong JIANG ,
  • Zhouchao WEI ,
  • Jingping LU
Expand
  • 1. College of Science, Guilin University of Technology, Guilin 541004, China;
    2. School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan 430074, China

Received date: 2020-01-10

  Revised date: 2021-04-11

  Online published: 2021-10-21

Supported by

This work was supported by the National Natural Science Foundation of China (11772306), Natural Science Foundation of Guangxi Province (2018GXNSFAA281021), Guangxi Science and Technology Base Foundation (AD20159017), the Foundation of Guilin University of Technology (GUTQDJJ2017062) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGGC05).

Abstract

This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities, which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality. Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.

Cite this article

Yirong JIANG , Zhouchao WEI , Jingping LU . THE NONEMPTINESS AND COMPACTNESS OF MILD SOLUTION SETS FOR RIEMANN-LIOUVILLE FRACTIONAL DELAY DIFFERENTIAL VARIATIONAL INEQUALITIES[J]. Acta mathematica scientia, Series B, 2021 , 41(5) : 1569 -1578 . DOI: 10.1007/s10473-021-0510-9

References

[1] Barbu V. Nonlinear Differential Equations of Monotone Types in Banach Spaces. London:Springer, 2010
[2] Fan Z B. Characterization of compactness for resolvents and its applications. Applied Mathematics and Computation, 2014, 232:60-67
[3] Heymans N, Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta, 2006, 45:765-771
[4] Jiang Y R, Huang N J, Wei Z C. Existence of a global attractor for fractional differential hemivariational inequalities. Discrete and Continuous Dynamical Systems Series B, 2020, 25(4):1193-1212
[5] Ke T D, Loi N V, Obukhovskii V. Decay solutions for a class of fractional differential variational inequalities. Fractional Calculus and Applied Analysis, 2015, 18(3):531-553
[6] Ke T D, Tuan T V. An indentification problem involving fractional differential variational inequalities. Journal of Inverse and Ill-Posed Problems, 2021, 29(2):185-202
[7] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations. Amsterdam:Elsevier, 2006
[8] Li X S, Huang N J, O'Regan D. A class of impulsive differential variational inequalities in finite dimensional spaces. Journal of the Franklin Institute, 2016, 353(13):3151-3175
[9] Li K X, Peng J G. Fractional resolvents and fractional evolution equations. Applied Mathematics Letters, 2012, 25:808-812
[10] Liu Z H, Motreanu D, Zeng S D. Nonlinear evolutionary systems driven by mixed variational inequalities and its applications. Nonlinear Analysis:Real World Applications, 2018, 42:409-421
[11] Loi N V, Ke T D, Obukhovskii V, Zecca P. Topological methods for some classes of differential variational inequalities. Journal of Nonlinear and Convex Analysis, 2016, 17:403-419
[12] Loi N V, Vu M Q. Uniqueness and Hyers-Ulam stability results for differential variational inequalities with nonlocal conditions. Differential Equations and Dynamical Systems, 2018, https://doi.org/10.1007/s12591-018-0429-3
[13] Migórski S, Zeng S D. Mixed variational inequalities driven by fractional evolutionary equations equations. Acta Mathematica Scientia, 2019, 39B(2):461-468
[14] Pang J S, Stewart D E. Differential variational inequalities. Mathematical Programming, 2008, 113(2):345-424
[15] Stewart D E. Dynamics with Inequalities:Impacts and Hard Constraints. Philadelphia:SIAM, 2011
[16] Weng Y H, Li X S, Huang N J. A fractional nonlinear evolutionary delay system driven by a hemi-variational inequality in Banach spaces. Acta Mathematica Scientia, 2021, 41B(1):187-206
[17] Ye H P, Gao J M, Ding Y S. A generalized Gronwall inequality and its application to a fractional differential equation. Journal of Mathematical Analysis and Applications, 2007, 328:1075-1081
[18] Zeng S D, Liu Z H, Migórski S. A class of fractional differential hemivariational inequalities with application to contact problem. Zeitschrift Für Angewandte Mathematik Und Physik, 2018, 69(2):36
[19] Zhu S G, Fan Z B, Li G. Topological characteristics of solution sets for fractional evolution equations and applications to control systems. Topological Methods in Nonlinear Analysis, 2019, 54(1):177-202
Options
Outlines

/