Decay mild solutions of Hilfer fractional differential variational–hemivariational inequalities

• Published in: Nonlinear analysis: real world applications Vol. 71; p. 103834
• Main Authors: Pang, Xia, Li, Xiuwen, Liu, Zhenhai
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2023
• Subjects: Decay mild solution; Hilfer fractional differential variational–hemivariational inequalities; History-dependent operator; Measure of noncompact; Mittag-Leffler function; History-dependent operator; Measure of noncompact; Hilfer fractional differential variational–hemivariational inequalities; Mittag-Leffler function; Decay mild solution
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2023.103834

The primary objective of this paper is to explore a decay mild solution governed by a class of dynamical systems, called Hilfer fractional differential variational–hemivariational inequality (HFDVHVI, for short), which is composed of a Hilfer fractional evolution differential inclusion and a variational–hemivariational inequality involving two history-dependent operators in the framework of spaces. Our first aim is to investigate the solvability of the mild solutions to (HFDVHVI) by means of fixed point principle. The second step of the paper is to study the existence of decay mild solutions to (HFDVHVI) via giving expression for the Mittag-Leffler function and the Wright function.