Spectral decomposition of the fractional Sturm–Liouville operator with $\rho $-generalized derivative
Volume 51 / 2024
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.
