Novel Fractional-Order Difference Schemes Reducible to Standard Integer-Order Formulas

In this letter, we advise numerical schemes for calculation of fractional derivatives of Grunwald-Letnikov type that reduce to standard integer-order derivative schemes. Since, in the literature, only forward differences have such a property, here, novel forms of backward differences and central differences based both on integer and half-integer mesh points are proposed. It enables the use of the proposed fractional differences interchangeably with standard difference formulas. The proposed schemes are qualitatively and quantitatively tested on 2-D signals for texture enhancement. The obtained results show that the proposed fractional differences provide better performances in comparison to traditional schemes.