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

TL;DR

This paper investigates a generalized Cauchy problem for an iterated multidimensional Klein-Gordon-Fock equation with a Bessel operator, reducing it to a polywave equation and deriving explicit solutions using fractional operators and spherical means.

Contribution

It introduces a novel approach using the Erdelyi-Kober fractional operator to solve a complex Klein-Gordon-Fock problem with a Bessel operator.

Findings

Explicit solution formula derived

Integral representation of the solution obtained

Reduction to a polywave equation achieved

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.