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Spectral decomposition of the fractional Sturm–Liouville operator with $\rho $-generalized derivative

Volume 51 / 2024

Abderachid Saadi, Mohamed Ourabah Benmeddour Applicationes Mathematicae 51 (2024), 75-93 MSC: Primary 26A33; Secondary 34K08, 34A08, 34Bxx, 47B40 DOI: 10.4064/am2482-5-2024 Published online: 22 July 2024

Abstract

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.

Authors

  • Abderachid SaadiDepartment of Mathematics
    University of M’sila
    PO Box 166 Ichebilia
    28000 M’sila, Algeria
    and
    Laboratory of Nolinear PDE
    ENS Kouba
    Algiers, Algeria
    e-mail
    e-mail
  • Mohamed Ourabah BenmeddourDepartment of Mathematics
    University of M’sila
    PO Box 166 Ichebilia
    28000 M’sila, Algeria
    e-mail

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