SOLUTION OF ONE CLASS OF MULTI-DIMENSIONAL INTEGRAL EQUATIONS OF THE FIRST KIND WITH MITTAG-LEFFLER FUNCTION IN KERNELS

One class of multidimensional integral equations of the first kind with Mittag-Leffler function in kernels over a bounded pyramidal domain of a special form is considered. Following the technique of Ya. Tamarkin, explicit formulas for the solution of the considered multidimensional integral equations are derived. Necessary and sufficient conditions for the solvability of such equations in spaces of summable functions are established.