A time-fractional diffusion equation with space-time dependent hidden-memory variable order: analysis and approximation
A time-fractional diffusion equation with space-time dependent hidden-memory variable order: analysis and approximation
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DOI：
10.1007/s10543-021-00861-4
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发表时间：
2021-04
影响因子：
1.5
通讯作者：
Xiangcheng Zheng;Hong Wang
中科院分区：
文献类型：
--
作者：
Xiangcheng Zheng;Hong Wang
研究了一类具有隐记忆时空相依变量阶的时间分数阶偏微分方程。通过预解式估计证明了问题的适定性和高阶正则性估计。在此基础上，分析了L-1离散化的误差估计。数值实验证实了理论结果，并研究了变阶分数阶偏微分方程的行为。
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.