Eigenvalue problem for fractional differential operator containing left and right fractional derivatives

Advances in Difference Equations

Wenbin Liu¹  Hua Jin¹ 

[1] Department of Mathematics, China University of Mining and Technology, Xuzhou, P.R. China

关键词: weak left (right) fractional derivative;    fractional Sobolev space;    regularity;    eigenvalue;    eigenfunction;    34A08;    34B09;    46E35;    58E05;   

DOI  :  10.1186/s13662-016-0950-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider the eigenvalue problem for fractional differential operator containing left and right fractional derivatives with Dirichlet boundary value conditions. By critical point theory, we see that there exist an eigenvalue sequence which is increasing, tending to infinity, and an eigenfunction sequence which is a Hilbert basis of a fractional Sobolev space.

【 授权许可】

CC BY