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arXiv · 1901.10376

On the fractional version of Leibniz rule

Paulo M. de Carvalho Neto·Renato Fehlberg Junior
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Abstract

This manuscript is dedicated to prove a new inequality that involves an important case of Leibniz rule regarding Riemann-Liouville and Caputo fractional derivatives of order $\alpha\in(0,1)$. In the context of partial differential equations, the aforesaid inequality allows us to address the Faedo-Galerkin method to study several kinds of partial differential equations with fractional derivative in the time variable; particularly, we apply these ideas to prove the existence and uniqueness of solution to the fractional version of the 2D Stokes equations in bounded domains.

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Paulo M. de Carvalho Neto, Renato Fehlberg Junior. 2019-01-29. On the fractional version of Leibniz rule. https://arxiv.org/abs/1901.10376

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