A Gronwall lemma for functions of two variables and its application to partial differential equations of fractional order

Dariusz Idczak

doi:10.3934/mcrf.2021019

Article Contents

2022, Volume 12, Issue 1: 225-243. Doi: 10.3934/mcrf.2021019

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A Gronwall lemma for functions of two variables and its application to partial differential equations of fractional order

Dariusz Idczak^,

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

^* Corresponding author: Dariusz Idczak
^* Corresponding author: Dariusz Idczak

Received: May 2020

Revised: January 2021

Early access: March 2021

Published: March 2022

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Abstract

In the paper, a new Gronwall lemma for functions of two variables with singular integrals is proved. An application to weak relative compactness of the set of solutions to a fractional partial differential equation is given.

Keywords:

Gronwall lemma,
singular integrals,
fractional partial differential equation.

Mathematics Subject Classification: Primary: 26B20; Secondary: 35R11.

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References

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