On the fractional integrals and derivatives of Bateman's matrix polynomials

TL;DR

This paper explores fractional integrals and derivatives of Bateman's matrix polynomials, deriving properties, integral representations, and recurrence relations for hypergeometric matrix functions using advanced integral transforms.

Contribution

It introduces new fractional integral formulas and matrix differential equations for hypergeometric matrix functions, expanding the theoretical framework for matrix polynomial analysis.

Findings

Derived properties and recurrence relations for hypergeometric matrix functions

Established integral representations using beta and Laplace transforms

Developed fractional integral formulas with Erdelyi Kober operators

Abstract

The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We introduce some matrix differential equations of the three order, integral transform and fractional integral formulas for hypergeometric matrix function by using the beta and Laplace transforms formula, Erdelyi Kober type fractional integral operators