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用再生核方法求解一类分数阶微分方程边界值问题

Using reproducing kernel method for solving a class of fractional differential

中文摘要英文摘要

在以前的工作中,我们之前主要从事再生核方面的研究,基于已经得到的科研成果,在这篇文章中,我们主要引进再生核方法并且用它来解决一类分数阶微分方程边界值问题。首先,对黎曼-刘维尔分数阶微分算子进行简要的介绍,然后,介绍了如何用再生核的方法来解决分数阶微分方程,在此之后,我们给出了几个典型的例子来说明这种方法的有效性,在文章的最后,我们得出结论,再生核方法是一种有效的数值方法。

In our previous work, we devoted our major work into the reproducing kernel method, based on the work we have done, in this paper, we mainly introduce this effective numerical method and use it to solve a class of fractional differential equations. At the beginning of the paper, we first give out the definition of the Riemann-Liouville fractional differential operator, then, introduce the main idea of how to use the reproducing kernel method to solve the fractional differential equations, after that, we give some famous examples to show the effective of it, at the end of this paper, we draw a conclusion that reproducing kernel method is an effective method.

屈杉山、王玉兰、于浩

数学

计算数学再生核方法分数阶微分方程边界是问题解析解

omputational mathematicsreproducing kernel methodfractional differential equationsboundary value problemsanalytical solution.

屈杉山,王玉兰,于浩.用再生核方法求解一类分数阶微分方程边界值问题[EB/OL].(2014-06-17)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/201406-275.点此复制

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