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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

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

* Corresponding author: Dariusz Idczak

Received  May 2020 Revised  January 2021 Early access March 2021

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.

Citation: Dariusz Idczak. A Gronwall lemma for functions of two variables and its application to partial differential equations of fractional order. Mathematical Control & Related Fields, doi: 10.3934/mcrf.2021019
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