Index transforms with Weber type kernels

TL;DR

This paper introduces new index transforms with Weber type kernels involving Bessel functions, analyzes their properties in Lebesgue spaces, and applies them to solve a boundary value problem for a fourth order PDE.

Contribution

It develops novel index transforms with Weber type kernels, providing their mapping and inversion formulas, and demonstrates their application to boundary value problems.

Findings

Established mapping properties in Lebesgue spaces

Derived inversion formulas for the transforms

Applied transforms to solve a boundary value problem

Abstract

New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth order partial differential equation.