The Saigo operator applied to some special functions

Abstract

The Saigo fractional operators are defined using the Gauss hypergeometric functions as kernel. They generalize Riemann-Liouville, Erdélyi-Kober and Weyl operators. In this article, Saigo operators are applied to the following special functions: Generalized hypergeometric function, generalization of Hermite's polynomials and Laguerre's polynomials.

Keywords

• fractional differentiation and integration operators
• hypergeometric function