On the fractional Laplacian of variable order
- Stanford Univ., CA (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Univ. of Bari Aldo Moro (Italy)
- Eidgenoessische Technische Hochschule (ETH), Zurich (Switzerland)
We present a novel definition of variable-order fractional Laplacian on Rn based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson’s equation involving this operator and we compute the corresponding Green’s function, for which we provide some instructive examples for specific problems.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- DOE Contract Number:
- NA0003525
- OSTI ID:
- 1821967
- Report Number(s):
- SAND2021-10850R; 699959
- Country of Publication:
- United States
- Language:
- English
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