Analog of the Cauchy Problem for the inhomogeneous manydimensional polycaloric equation with Bessel operator

TL;DR

This paper derives an explicit solution formula for an inhomogeneous multi-dimensional polycaloric equation with a Bessel operator, utilizing Erdelyi-Kober fractional operators to extend classical Cauchy problem methods.

Contribution

It introduces a novel explicit solution formula for the polycaloric equation with Bessel operators using Erdelyi-Kober fractional calculus.

Findings

Explicit solution formula derived for the inhomogeneous polycaloric equation

Application of Erdelyi-Kober fractional operators in constructing solutions

Extension of classical Cauchy problem methods to Bessel operator context

Abstract

In the work an explicit formula of a solution of analogue of a Cauchy problem for an inhomogeneous manydimensional polycaloric equation with Bessel operator was found. Manydimensional Erdelyi-Kober operator of the fractional order was applied to construction of a solution