On (<i>q</i>, <i>h</i>)-Analogue of Fractional Calculus

Abstract

The paper discusses fractional integrals and derivatives appearing in the so-called (q, h)-calculus which is reduced for h = 0 to quantum calculus and for q = h = 1 to difference calculus. We introduce delta as well as nabla version of these notions and present their basic properties. Furthermore, we give comparisons with the known results and discuss possible extensions to more general settings.