Multiplication of fractional calculus operators and boundary value problems involving the Euler-Darboux equation

Abstract

With a view to presenting solutions of various boundary value problems involving the celebrated Euler-Darboux equation, the authors consider the multiplication of certain classes of operators of fractional calculus defined in terms of the Gaussian hypergeometric function. The fractional calculus operators studied here incorporate, as their special cases, both the Riemann-Liouville and Erdélyi-Kober operators, and are appropriately restricted in order to yield explicit solutions of some of the aforementioned boundary value problems in terms of Appell functions and Kampé de Fériet functions of two variables.