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.
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
[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