The inversion formula for the Volterra integral equation with the Humbert function in the nuclear and its applications to the boundary value problems

TL;DR

This paper introduces an inversion formula for a Volterra integral equation with a Humbert function kernel, facilitating solutions to boundary value problems in applied mathematics.

Contribution

It presents a novel inversion formula involving a degenerate hypergeometric function of two variables for solving a specific Volterra integral equation.

Findings

Derived an explicit inversion formula for the integral equation

Expressed solutions using a new hypergeometric function of two variables

Applied the formula to boundary value problems in PDEs

Abstract

Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving boundary value problems for second-order partial differential equations. In this paper, we introduce one degenerate hypergeometric function of two variables through which the solution of the Volterra integral equation of the first kind studing here is expressed.