Generalized fractional operator representations of Jacobi type orthogonal polynomials

TL;DR

This paper introduces generalized fractional operators involving Appell's function to analyze Jacobi-type orthogonal polynomials, expressing results through hypergeometric functions and exploring special cases.

Contribution

It develops new fractional operator representations for Jacobi polynomials using Appell's function, extending existing mathematical frameworks.

Findings

Derived fractional operator formulas for Jacobi polynomials

Expressed results in terms of generalized hypergeometric functions

Identified special cases with simplified expressions

Abstract

The aim of this paper is to apply generalized operators of fractional integration and differentiation involving Appell's function $F_{3}(:)$ due to Marichev-Saigo-Maeda (MSM), to the Jacobi type orthogonal polynomials. The results are expressed in terms of generalized hypergeometric function. Some of the interesting special cases of the main results also established.