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.
- Bessel potential spaces
- Fractional gradient
- fractional Sobolev inequalities
- fractional partial differential equations
ASJC Scopus subject areas
- Applied Mathematics