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

Fethi Bouzeffour; Fethi Bouzeffour

doi:10.3934/math.2025833

AIMS Mathematics

2025, Volume 10, Issue 8: 18641-18659. doi: 10.3934/math.2025833

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

Fethi Bouzeffour ^,

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

Received: 07 June 2025 Revised: 12 August 2025 Accepted: 14 August 2025 Published: 18 August 2025
MSC : 26A33, 42B10

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.
- fractional Jacobi differential operators,
- Fourier–Jacobi integral transform,
- operational calculus
Citation: Fethi Bouzeffour. On the singular integral representation of the fractional powers of Jacobi differential operators[J]. AIMS Mathematics, 2025, 10(8): 18641-18659. doi: 10.3934/math.2025833

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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.

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