On composition of some general fractional integral operators (Q1331184)

The authors derive three interesting expressions for the composition of two general fractional integral operators whose kernel involve the product of a general class of polynomials and a multivariable \(H\)- function. By suitably specializing the coefficients and the parameters in these functions a large number of (new and known) useful expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions involving one or more variables can be obtained. The authors have mentioned two special cases of their first composition formula. The present study unifies and extends a large number of results lying scattered in the literature.