Exact Solutions for a Partial System of Second-Order Hypergeometric Equations and Some Decomposition Formulas

In this article, some types of partial differential equations of applied mathematics are considered. It is important for us to study exact solutions of the systems of partial differential equations that are satisfied by hypergeometric functions of many variables. So, it were founded sixteen explicit exact solutions of such system of partial differential equations. In concrete, we consider the Sharma and Parihar’s function among well-known eighty three hypergeometric functions and show how to find exact solutions for partial differential equations in the form of hypergeometric functions. For the function $$F_{2}^{(4)}\big{(}a_{1},a_{2},b;c_{1},c_{2},c_{3},c_{4};x,y,z,t\big{)}$$ four integral representations and three decomposition formulas are obtained by the aid of classical methods.

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