Numerical discretization of Riemann–Liouville fractional derivatives with strictly positive eigenvalues

Sam Motsoka Rametse; Rhameez Sheldon Herbst

doi:10.3390/ appliedmath5040130

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$Numerical discretization of Riemann–Liouville fractional derivatives with strictly positive eigenvalues$

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Numerical discretization of Riemann–Liouville fractional derivatives with strictly positive eigenvalues

Sam Motsoka Rametse and Rhameez Sheldon Herbst

2026

DOI: https://doi.org/10.3390/ appliedmath5040130

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https://hdl.handle.net/10210/519218

Abstract

Riemann–Liouville fractional derivative

fractional Calculus

spectral analysis

This paper investigates a unique and stable numerical approximation of the Riemann– Liouville Fractional Derivative. We utilize diagonal norm finite difference-based time integration methods within the summation-by-parts framework. The second-order accurate discretizations developed in this study are proven to possess eigenvalues with strictly positive real parts for non-integer orders of the fractional derivative. These results lead to provably invertible, fully discrete approximations of Riemann–Liouville derivatives.

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Title: Numerical discretization of Riemann–Liouville fractional derivatives with strictly positive eigenvalues
Creators - without role: Sam Motsoka Rametse
Rhameez Sheldon Herbst
Identifiers: 9960907407691
Academic Unit: University of Johannesburg; Faculty of Science; Department of Mathematics and Applied Mathematics
Language: English
Resource Type: Journal article