T. S. Aleroev, H. T. Aleroeva, Ning-Ming Nie, and Yi-Fa Tang

Boundary Value Problems for Differential Equations of Fractional Order

abstract:
We carry out spectral analysis of a class of integral operators associated with fractional order differential equations arising in mechanics. We establish a connection between the eigenvalues of these operators and the zeros of Mittag-Leffler type functions. We give sufficient conditions for complete nonselfadjointness and completeness of the systems of the eigenfunctions. We prove the existence and uniqueness of solutions for several kinds of two-point boundary value problems for fractional differential equations with Caputo or Riemann-Liouville derivatives, and design single shooting methods to solve them numerically.

Mathematics Subject Classification: 34K

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