A generalized multiparameter function of Mittag-Leffler type

In this paper, we define and study a generalized multiparameter function of Mittag-Leffler type. Some special cases and basic properties including its Mellin–Barnes-type integral representation, recurrence relation, and expansion are given. The Laplace transform and the first Sonine integral of the generalized function are evaluated. Differential and integral equations with the Erdelyi–Kober operator are established. The Cauchy problem for the multiparameter differential equation is formulated and its solution is obtained.