Generalised differences and their applications (Q1076205)

In this paper a generalized difference operator \(A^{\lambda}_{\mu,h}\) of order \(\lambda\) and step \(h>0\), where \(\lambda\) and \(\mu\) are arbitrary real numbers, is defined in such a way that the forward, and central difference operators become its particular cases. A Leibniz formula for the operator is given and illustrated with its help certain known results. The operator also leads to a fractional derivatives of powers. This derivatives of powers is compared with some other known fractional derivatives.