Abstract

A problem of functions factorization is studied with respect to the fundamental solution of a fractional generalization of the Helmholtz equation. A factorization technique that is applicable for a wide class of functions represented by the Mellin–Barnes type integral is proposed. Factorized representations in integral form and in terms of the H-function are obtained for the fundamental solution of the considered equation.

中文翻译：

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分数亥姆霍兹方程基本解的因式分解

摘要

关于Helmholtz方程的分数一般化的基本解，研究了函数分解的问题。提出了一种分解方法，该技术适用于以Mellin-Barnes型积分表示的各种函数。对于所考虑的方程的基本解，获得了积分形式和H函数形式的因式分解表示。