Composition formulas of Bessel-Struve kernel function

TL;DR

This paper derives composition formulas and integral representations for the Bessel-Struve kernel function using fractional operators involving Appell's function, connecting it to generalized Wright functions.

Contribution

It introduces new composition formulas and integral representations for the Bessel-Struve kernel function using fractional calculus and special functions.

Findings

Derived composition formulas involving fractional operators and Bessel-Struve kernel.

Obtained integral representations of the Bessel-Struve kernel function.

Established relations between the Bessel-Struve kernel and other special functions.

Abstract

The generalized operators of fractional integration involving Appell's function $F_{3}(.) $ due to Marichev-Saigo-Maeda, is applied to the Bessel Struve kernel function $S_{\alpha }\left( \lambda z\right),\lambda ,z\in \mathbb{C}$ to obtain the results in terms of generalized Wright functions.The pathway integral representations Bessel Struve kernel function and its relation between many other functions also derived in this study.