Solution of the analogue of the Cauchy problem for the iterated multidimensional Klein-Gordon-Fock equation with the Bessel operator

Abstract

An analogue of the Cauchy problem for the iterated multidimensional Klein- Gordon-Fock equation with a time-dependent Bessel operator is investigated. Applying the generalized Erdelyi-Kober operator of fractional order, the problem posed is reduced to the Cauchy problem for the polywave equation. An explicit formula for solving this problem is constructed by the spherical mean method. On the basis of the solution obtained, an integral representation of the solution of the problem is found.