The Cauchy Problem for Erdelyi-Kober Operators

Abstract

It is well known that Mikusinski’s operational calculus can be used in solution of linear differential equations with constant and polynomial coefficients and in solution of some partial differential equations with constant coefficients. In this chapter we will obtain exact solutions of some class of integro-differential equations with multiple Erdelyi-Kober fractional differentiation operator (18.16) which contains, as we have seen in Chapter 18, among particular cases both the Riemann-Liouville fractional differentiation operator (18.19) and the hyper-Bessel differential operator (18.17). Consequently, as particular cases we will obtain exact solutions of the differential equations of fractional order with constant coefficients and the differential equations of hyper-Bessel type.