×

zbMATH — the first resource for mathematics

Boundary value problem for differential equation with fractional order derivatives with different origins. (Russian. English summary) Zbl 1413.34017
Summary: 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 \(L_{2}\left(0,1\right)\).

MSC:
34A08 Fractional ordinary differential equations
34L05 General spectral theory of ordinary differential operators
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34B08 Parameter dependent boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI MNR
References:
[1] [1] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp. · Zbl 1066.26005
[2] [2] S. Sh. Rekhviashvili, “K opredeleniyu fizicheskogo smysla drobnogo integro- differentsirovaniya”, Nelineinyi mir, 5:4 (2007), 194–197
[3] [3] S. Sh. Rekhviashvili, “Formalizm Lagranzha s drobnoi proizvodnoi v zadachakh mekhaniki”, Pisma v ZhTF, 30:2 (2004), 33–37
[4] [4] B. Stanković, “An equation with left and right fractional derivatives”, Publications de l’institute mathématique, Nouvelle série, 94:80 (2006), 259–272 · Zbl 1246.26008
[5] [5] T. M. Atanackovic, B. Stankovic, “On a differential equation with left and right fractional derivatives”, Fractional calculus and applied analysis, 10:2 (2007), 139–150 · Zbl 1136.26301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.