T. S. Aleroev and H. T. Aleroeva

Some Applications of the Perturbation Theory to Fractional Calculus

abstract:
Spectral analysis of a class of integral operators associated with fractional order differential equations arising in mechanics is carried out. The connection between the eigenvalues of these operators and zeros of Mittag-Leffler type functions is established. Sufficient conditions for complete non-self-adjointness and completeness of the systems of eigenfunctions are given.

Mathematics Subject Classification: 34K

Key words and phrases: Caputo's derivatives, Riemann-Liouville derivatives, fractional differential equation, two-point boundary value problem