@article{Bouzeffour2025, 
author = {Fethi Bouzeffour},
title = {On the singular integral representation of the fractional powers of Jacobi differential operators},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {18641-18659},
keywords = {fractional Jacobi differential operators, Fourier–Jacobi integral transform, operational calculus},
url = {https://www.sciopen.com/article/10.3934/math.2025833},
doi = {10.3934/math.2025833},
abstract = {In this paper, we introduce the fractional Jacobi operator and present its formulation in terms of a pseudo-differential operator via the Fourier–Jacobi transform. Furthermore, by employing the generalized shift operator related to the Jacobi operator, we establish a singular integral representation of the fractional Jacobi operator.}
}