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- W4293777195 abstract "introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green's identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus." @default.
- W4293777195 created "2022-08-31" @default.
- W4293777195 creator A5028709260 @default.
- W4293777195 date "2021-07-01" @default.
- W4293777195 modified "2023-09-26" @default.
- W4293777195 title "A Unified Theory of Fractional and Nonlocal Calculus." @default.
- W4293777195 doi "https://doi.org/10.2172/1884224" @default.
- W4293777195 hasPublicationYear "2021" @default.
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