Topological Structure of Solution Set to a Fractional Differential Inclusion Problem with Delay

Symmetry

Shanshan Gao¹  Bin Ge¹  Rui Wu² 

[1] College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China;Department of Mathematics, Changchun University of Finance and Economics, Changchun 130000, China;

关键词: topological structure;    fractional differential inclusion;    Rδ-set;    inverse limit method;    nonlocal problems;    symmetry;   

DOI  :  10.3390/sym14040792

来源: DOAJ

【 摘 要 】

In this paper, we investigate the topological structure of the solution set to a fractional differential inclusion with delay defined on the half-line. We first prove that the solution set to the inclusion is an $R_{\delta }$-set on compact intervals. Then, by means of the inverse limit method, we generalize our results to noncompact intervals. Moreover, under convex and nonconvex conditions, an $R_{\delta }$-property solution set is obtained for some nonlocal problems, where the nonlocal function is set-valued. Further, we study the symmetry of the solution set under some conditions.

【 授权许可】

Unknown