A Description of Derivation Operators with Respect to Convolution of Generalized Gel’Fond-Leont’Ev Integration

Abstract

Abstract We describe all solutions of the operator analogue of the product rule with respect to a convolution of the generalized Gel’fond-Leont’ev integration in the space of functions analytic in a domain of the complex plane. This is an important example of the Erdélyi-Kober operator of integration of fractional order, for which a series of basic results have been proposed by Dimovski and Kiryakova, and in a series of previous authors’ papers