On generalized Mittag—Leffler type functions of three variables

We study some properties of one of the Mittag—Leffler type functions generated by generalizing three-variable Lauricella hypergeometric functions. Mainly special cases, integral representations of the Euler type are proved, one dimensional and three dimetional Laplace transforms of the function also determined. We have also constructed a system of partial differential equations which is linked with this function, Riemann—Liouville fractional integral and derivative are calculated.