On some geometric interpretations of fractional-order operators

2024/11/19 by Igor Podlubný, Podlubny, Igor
Mathematics · #01A55 #01A65 (Secondary) #26A33 (Primary) 01A45 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fractional Differential Equations Solutions #History and Overview (math.HO) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2411.12494

openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This discussion paper presents some parts of the work in progress. It is shown that G.W. Leibniz was the first who raised the question about geometric interpretation of fractional-order operators. Geometric interpretations of the Riemann--Liouville fractional integral and the Stieltjes integral are explained. Then, for the first time, a geometric interpretation of the Stieltjes derivatives is introduced, which holds also for so-called ``fractal derivatives'', which are a particular case of Stieltjes derivatives.

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