Proof of the completeness of the system of eigenfunctions for one boundary-value problem for the fractional differential equation

• Main Authors: Mukhamed Aleroev, Hedi Aleroeva, Temirkhan Aleroev
• Format: Article
• Language: English
• Published: AIMS Press 2019-06-01
• Series: AIMS Mathematics
• Subjects: Mittag-Leffler function; spectrum; eigenvalue; fractional derivative; completeness
• Online Access: https://www.aimspress.com/article/10.3934/math.2019.3.714/fulltext.html
• ISSN: 2473-6988

The present paper is devoted to the spectral analysis of operators induced by differential expressions of fractional order and boundary conditions of Sturm-Liouville type. In particular, this paper establishes the completeness of the system of eigenfunctions and associated functions of one class for non-self-adjoint integral operators associated with boundary-value problems for fractional-order differential equations.