On a Generalization of Sobolev-Slobodecki Spaces and an Associated Fractional Derivative
4 Pages Posted: 27 Nov 2018
Date Written: July 1, 2018
Abstract
In this article, we present a new kind of fractional derivative D and fractional integral I, which are related to a generalization W s,q(Ω; ∂Ω) of Sobolev-Slobodecki spaces and satisfy a kind of fractional divergence theorem ∫∂Ω(Iv)(y) dS (y) = ∫Ω(Dν)(x) dx for functions ν∈ W s,q(Ω; ∂Ω). Further, we show how this space occurs in a discussion of linear elliptic equations with singular Neumann boundary data.
Suggested Citation: Suggested Citation
Merker, Jochen, On a Generalization of Sobolev-Slobodecki Spaces and an Associated Fractional Derivative (July 1, 2018). Proceedings of International Conference on Fractional Differentiation and its Applications (ICFDA) 2018, Available at SSRN: https://ssrn.com/abstract=3270836 or http://dx.doi.org/10.2139/ssrn.3270836
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