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arXiv · 1709.01113

The mean value theorems and a Nagumo-type uniqueness theorem for Caputo's fractional calculus (Corrected Version)

Kai Diethelm
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Abstract

We generalize the classical mean value theorem of differential calculus by allowing the use of a Caputo-type fractional derivative instead of the commonly used first-order derivative. Similarly, we generalize the classical mean value theorem for integrals by allowing the corresponding fractional integral, viz.\ the Riemann-Liouville operator, instead of a classical (first-order) integral. As an application of the former result we then prove a uniqueness theorem for initial value problems involving Caputo-type fractional differential operators. This theorem generalizes the classical Nagumo theorem for first-order differential equations.

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Kai Diethelm. 2017-09-04. The mean value theorems and a Nagumo-type uniqueness theorem for Caputo's fractional calculus (Corrected Version). https://arxiv.org/abs/1709.01113

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