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arXiv · 2411.12494

On some geometric interpretations of fractional-order operators

Igor Podlubny
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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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Igor Podlubny. 2024-11-19. On some geometric interpretations of fractional-order operators. https://arxiv.org/abs/2411.12494

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