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Eigenvalue problems for fractional ordinary differential equations. (English) Zbl 1258.34041

Summary: The eigenvalue problems are considered for the fractional ordinary differential equations with different classes of boundary conditions including the Dirichlet, Neumann, Robin boundary conditions and the periodic boundary condition. The eigenvalues and eigenfunctions are characterized in terms of the Mittag-Leffler functions. The eigenvalues of several specified boundary value problems are calculated by using MATLAB subroutine for the Mittag-Leffler functions. When the order is taken as the value 2, our results degenerate to the classical ones of the second-ordered differential equations. When the order \(\alpha \) satisfies \(1 < \alpha < 2\), there can be finitely many eigenvalues.

MSC:

34B09 Boundary eigenvalue problems for ordinary differential equations
34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
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