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arXiv · 2309.07148

An extension of the Cartwright-McMullen theorem in fractional calculus for the smooth Stieltjes case

Daniel Cao Labora
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Abstract

In 1976, Donald Cartwright and John McMullen characterized axiomatically the Riemann-Liouvile fractional integral in a paper that was published in 1978. The motivation for their work was to answer affirmatively to a conjecture stated by J. S. Lew a few years before, in 1972. Essentially, their ``Cartwright-McMullen theorem in fractional calculus'' proved that the Riemann-Liouville fractional integral is the only continuous extension of the usual integral operator to positive real orders, in such a way that the Index Law holds. In this paper, we propose an analogous result for the uniqueness of the extension of the Stieltjes integral operator, in the case of a smooth integrator.

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Daniel Cao Labora. 2023-09-07. An extension of the Cartwright-McMullen theorem in fractional calculus for the smooth Stieltjes case. https://arxiv.org/abs/2309.07148

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