In this paper, we study the elementary solution of the operator  which is iterated k-times and is defined by

where m is a positive real number and  is the dimension of the n-dimensional Euclidean space  and k is a nonnegative integer. At first, we study the elementary solution of the operator  Moreover, the operator  can be related to the Laplace operator  and the ultra-hyperbolic Klein Gordon operator, and also we obtain the elementary solutions of such operators. We also apply such an elementary solution to obtain the solution of the equation  where  is a generalized function and  is an unknown function for

elementary solution, ultra-hyperbolic Klein Gordon operator, Dirac delta distribution.