Abstract
A time-fractional partial differential equation with a hidden-memory space-time dependent variable order is studied. The well-posedness and high-order regularity estimates of the problem are proved via the resolvent estimates. Accordingly, an error estimate of the L-1 discretization without any artificial regularity assumption of the true solution is analyzed. Numerical experiments are performed to substantiate the theoretical results and to study the behavior of the variable-order fractional partial differential equations.
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The authors would like to express their most sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper. All data generated or analyzed during this study are included in this article.
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Communicated by Mihaly Kovacs.
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This work was partially funded by the ARO MURI Grant W911NF-15-1-0562 and the National Science Foundation under Grant DMS-2012291.
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Zheng, X., Wang, H. A time-fractional diffusion equation with space-time dependent hidden-memory variable order: analysis and approximation. Bit Numer Math 61, 1453–1481 (2021). https://doi.org/10.1007/s10543-021-00861-4
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DOI: https://doi.org/10.1007/s10543-021-00861-4
Keywords
- Time-fractional diffusion equation
- Space-time dependent variable order
- Well-posedness
- Regularity
- L-1 discretization
- Error estimates