(untitled) (European Journal of Pure and Applied Mathematics, 2021)
In this article, we study the fundamental solution of the operator _m^k, iterated k-times and is defined by_m^k = [(_r=1^p ^2 x_r^2+m^2)^4 - ( _j=p+1^p+q ^2x_j^2 )^4 ]^k, where m is a nonnegative real number, p+q=n is the dimension of the Euclidean space R^n,x=(x_1,x_2,…,x_n)R^n, k is a nonnegative integer. At first we study the fundamental solution of the operator _m^k and after that, we apply such the fundamental solution to solve for the solution of the equation _m^ku(x)= f(x), where f(x) is generalized function and u(x) is unknown function for xR^n.