Geometric behavior of the generalized Hadid-Luchko convolution operator in the open unit ball

In this effort, by consuming the k-symbol calculus, we generalize the Hdid-Luchko function (the Mittag-Leffler function of several variables). Some inequalities are established containing the normalized type of this function. In addition, we illustrate a list of conditions on the function to recognize some special geometric properties in a unit ball. Our theory is based on the differential subordination of several variables.