Solutions of systems of the partial differential equations of Kamp\'e de F\'eriet type functions

TL;DR

This paper derives explicit solutions for systems of partial differential equations involving Kampé de Fériet hypergeometric functions of third and fourth order in two variables, aiding in boundary-value problem analysis.

Contribution

It provides new explicit solutions for PDE systems associated with Kampé de Fériet functions of higher order, expanding the analytical tools available for such equations.

Findings

Explicit solutions for third and fourth order systems

Solutions applicable to boundary-value problems

Enhanced understanding of hypergeometric PDE systems

Abstract

In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. In this present investigation, we give the solutions of systems of partial differential equations for two Kamp\'e de F\'eriet type functions of third and fourth orders and of two variables.