Geodesic
Spectral decomposition of the fractional Sturm–Liouville operator with $\rho $-generalized derivative
Abderachid Saadi 1   ; Mohamed Ourabah Benmeddour 2
1 Department of Mathematics University of M’sila PO Box 166 Ichebilia 28000 M’sila, Algeria and Laboratory of Nolinear PDE ENS Kouba Algiers, Algeria
2 Department of Mathematics University of M’sila PO Box 166 Ichebilia 28000 M’sila, Algeria
Applicationes Mathematicae, Tome 51 (2024) no. 1, pp. 75-93 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the $\rho $-generalized fractional version of the classical Sturm–Liouville operator. We establish the existence and uniqueness of a boundary value problem for this operator with homogeneous boundary conditions. Using this problem, we present a spectral decomposition of the $\rho $-generalized fractional Sturm–Liouville operator.
DOI : 10.4064/am2482-5-2024
Keywords: study rho generalized fractional version classical sturm liouville operator establish existence uniqueness boundary value problem operator homogeneous boundary conditions using problem present spectral decomposition rho generalized fractional sturm liouville operator

Abderachid Saadi  1   ; Mohamed Ourabah Benmeddour  2

1 Department of Mathematics University of M’sila PO Box 166 Ichebilia 28000 M’sila, Algeria and Laboratory of Nolinear PDE ENS Kouba Algiers, Algeria
2 Department of Mathematics University of M’sila PO Box 166 Ichebilia 28000 M’sila, Algeria 
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     journal = {Applicationes Mathematicae},
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Abderachid Saadi; Mohamed Ourabah Benmeddour. Spectral decomposition of the fractional Sturm–Liouville operator with $\rho $-generalized derivative. Applicationes Mathematicae, Tome 51 (2024) no. 1, pp. 75-93. doi: 10.4064/am2482-5-2024

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