A convolution family in the Dimovski sense for the composed Erdélyi-Kober fractional integrals

Abstract

ABSTRACTIn this paper, we first introduce suitable compositions of the right- and left-hand sided Erdélyi-Kober fractional integrals and derivatives that we call composed Erdélyi-Kober fractional integrals and derivatives. These operators play an important role while treating the fractional differential equations containing both the right- and the left-hand sided Erdélyi-Kober fractional derivatives. One of possible strategies for solving these equations is to apply a kind of operational calculus for the composed Erdélyi-Kober fractional derivatives. The first step in development of such operational calculus in Mikusiński sense consists in construction of a suitable convolution. In this paper, a one-parametric family of convolutions in the Dimovski sense for the composed Erdélyi-Kober fractional integrals is constructed.