On a new class of fractional partial differential equations

In this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to extend many classical results in the Sobolev spaces to the nonl...

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Bibliographic Details
Main Authors Shieh, Tien-Tsan, Spector, Daniel
Format Journal Article
LanguageEnglish
Published 31.03.2014
Subjects
Mathematics - Analysis of PDEs
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Summary:In this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to extend many classical results in the Sobolev spaces to the nonlocal and fractional setting in a natural way.
DOI:10.48550/arxiv.1403.7942