On the fractional version of Leibniz rule

2019/01/29 by Neto, Paulo M. de Carvalho, Junior, Renato Fehlberg · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.10376

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 α∈(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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