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Research Article | Open Access

On the singular integral representation of the fractional powers of Jacobi differential operators

Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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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.

Keywords

fractional Jacobi differential operatorsFourier–Jacobi integral transformoperational calculus
CLC number: 26A33, 42B10

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AIMS Mathematics
Volume 10 Issue 8,
August 2025
Pages 18641-18659
DOI: 10.3934/math.2025833

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Bouzeffour F. On the singular integral representation of the fractional powers of Jacobi differential operators. AIMS Mathematics, 2025, 10(8): 18641-18659. https://doi.org/10.3934/math.2025833

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Received: 07 June 2025
Revised: 12 August 2025
Accepted: 14 August 2025
Published: 15 August 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)