FRACTIONAL CENTRAL DIFFERENCES AND DERIVATIVES

Fractional central differences and derivatives are proposed in this paper. The positive even and odd integer orders differences and derivatives are generalised to real orders, obtaining two new different types of differences and derivatives. For each type, suitable integral formulation is obtained. Their computations of the integrals lead to generalisations of the well known Riesz potentials. A study for coherence is done by applying the definitions to functions with Fourier transform.