Analysis of Tempered Fractional Operators
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Tempered fractional operators provide an improved predictive capability for modeling anomalous effects that cannot be captured by standard partial differential equations. These effects include subdiffusion and superdiffusion (i.e. the mean square displacement in a diffusion process is proportional to a fractional power of the time), that often occur in, e.g., geoscience and hydrology. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators by means of a proper choice of the nonlocal kernel. Then, we present a plan for showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.
- Research Organization:
- Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1647701
- Report Number(s):
- SAND--2020-8275R; 689853
- Country of Publication:
- United States
- Language:
- English
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