On a Class of Positive Definite Operators and Their Application in Fractional Calculus

Abstract

This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary value problems for differential equations of fractional order. Approximation matrices are also investigated. In particular, the positive definiteness of the studied operators is shown, which makes it possible to select areas in the complex plane where there are no eigenvalues of these operators.

Keywords

• persymmetric matrix
• eigenvalues
• fractional derivative
• positive definiteness