### Abstract:

In this article, we study the solution of the equation ?_{B,c?}^{k}?_{B,c?}^{k}u(x)=? where u(x) is an unknown generalized function and ? is a Dirac-delta function, ?_{B,c?}^{k} and ?_{B,c?}^{k} are the Ultra-Hyperbolic Bessel Operator iterated k-times and are defined by?_{B,c?}^{k} = [(1/(c?))(B_{x?}+B_{x?}++B_{x_{p}})-(B_{x_{p+1}}++B_{x_{p+q}})]^{k}?_{B,c?}^{k} = [(1/(c?))(B_{x?}+B_{x?}++B_{x_{p}})-(B_{x_{p+1}}++B_{x_{p+q}})]^{k}, where p+q=n, B_{x_{i}}=((?)/(?x_{i}))+((2v_{i})/(x_{i}))(?/(?x_{i})), where 2v_{i}=2?_{i}+1, ?_{i}>-(1/2)[6], x_{i}>0, i=1,2,...,n,c? and c? is positive constant, k is a nonnegative integer and n is the dimension of the R_{n}?. Firstly, it is found that the solution u(x) depends on the conditions of p and q and moreover such a solution is related to the solution of the Ultra-Hyperbolic Bessel Operator iterated k-times.