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

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.