Erdélyi-Kober Fractional Integrals in the Many Real Scalar Variables Case

Abstract

When going from a one-variable function to many-variable function there is no unique one to one correspondence. Many types of multivariate functions can be considered when one has the preselected one-variable function. Hence there is nothing called the multivariate analogue of a univariate operator or univariate integral. Hence we construct one multivariate operator here which is analogous to a one variable Erdélyi-Kober fractional integral operator of the second kind or first kind. Other such analogues can be defined. The second kind fractional integrals will be considered first. In this chapter, multivariate case means the case of many real scalar variables.