On a new class of fractional partial differential equations

Tien-Tsan Shieh; Daniel Spector

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arXiv · 1403.7942

On a new class of fractional partial differential equations

Tien-Tsan Shieh·Daniel Spector

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Abstract

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.

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Tien-Tsan Shieh, Daniel Spector. 2014-03-31. On a new class of fractional partial differential equations. https://arxiv.org/abs/1403.7942

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