T. S. Aleroev and H. T. Aleroeva
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