Diffusive Representations for the Numerical Evaluation of Fractional Integrals

TL;DR

This paper introduces a unified approach to diffusive representations of Riemann-Liouville fractional integrals, enabling the selection of optimal numerical methods based on detailed analytic properties for efficient computation.

Contribution

It presents a general framework encompassing various diffusive representations, facilitating tailored numerical algorithms for fractional integrals.

Findings

Unified approach covers most existing variants

Enables selection of optimal numerical methods

Improves efficiency of fractional integral evaluation

Abstract

Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of such representations have been proposed. Concentrating on Riemann-Liouville integrals whose order is in (0,1), we here present a general approach that comprises most of these variants as special cases and that allows a detailed investigation of the analytic properties of each variant. The availability of this information allows to choose concrete numerical methods for handling the representations that exploit the specific properties, thus allowing to construct very efficient overall methods.