Eigenvalue problems for fractional ordinary differential equations |
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| Institution: | 1. Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, PR China;2. Jining Teachers College, Wulanchabu 012000, Inner Mongolia, PR China;3. College of Science, Shanghai Institute of Technology, Fengxian District, Shanghai 201418, PR China;1. ESIPP, University College Dublin, Ireland;2. Department of Mathematics, Cankaya University, Ankara, Turkey;3. Institute of Space Sciences, Magurele, Bucharest, Romania |
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| Abstract: | 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 α satisfies 1 < α < 2 the eigenvalues can be finitely many. |
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