Geodesic
Boundary value problem for differential equation with fractional order derivatives with different origins
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2015), pp. 39-44

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We study a spectral problem for an ordinary differential equation with composition of fractional order differentiation operators in Riemann-Liouville and Caputo senses with different origins. We prove that for the problem under study there exist infinite sequences of eigenvalues and eigenfunctions. All of the eigenvalues are real and positive, and the eigenfunctions form an orthogonal basis in $L_{2}\left(0,1\right)$.
Keywords: fractional derivative, boundary value problem, eigenvalue, eigenfunction. 
@article{VKAM_2015_2_a5,
     author = {L. M. Eneeva},
     title = {Boundary value problem for differential equation with fractional order derivatives with different origins},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {39--44},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2015_2_a5/}
}
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L. M. Eneeva. Boundary value problem for differential equation with fractional order derivatives with different origins. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2015), pp. 39-44. http://geodesic.mathdoc.fr/item/VKAM_2015_2_a5/