Symmetrical Sonin kernels in terms of the hypergeometric functions

TL;DR

This paper introduces a new class of symmetrical Sonin kernels for Laplace convolution transforms, derived using special functions like Wright and Horn hypergeometric functions, expanding the analytical tools for integral transforms.

Contribution

It defines symmetrical Sonin kernels and derives new and known kernels using the Sonin method and integral transforms, involving advanced special functions.

Findings

New symmetrical Sonin kernels expressed via Wright and Horn functions

Derivation of kernels using Sonin method and Laplace transforms

Extension of integral transform kernel classes with special functions

Abstract

In this paper, we introduce a new class of the kernels of the integral transforms of the Laplace convolution type that we call symmetrical Sonin kernels. For a symmetrical Sonin kernel given in terms of some elementary or special functions, its associated kernel has the same form with possibly different parameter values. Several known and new kernels of this type are derived by means of the Sonin method in the time domain and using the Laplace integral transform in the frequency domain. The new symmetrical Sonin kernels are provided in terms of the Wright function and some extensions of the Horn confluent hypergeometric functions in two variables.