Step-by-step integration for fractional operators

In this paper, an approach based on the definition of the Riemann-Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald-Letnikov operators. The proposed Riemann-Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann-Liouville fractional integral and derivative are governing by operators very similar to the Grunwald-Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann-Liouville discretisation technique and the Grunwald-Letnikov discrete operators, both techniques have been applied to: unit step functions, exponential functions and sample functions of white noise. (C) 2017 Elsevier B.V. All rights reserved.