具有Riesz-Feller分数阶算子的反常扩散方程边值问题的数值解
Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator
AI总结：
本文提出基于有限差分法的数值方法，求解具有Riesz-Feller分数阶导数的常微分方程边值问题，并模拟了纳米管中的非线性温度分布。
摘要：
本文提出了一维空间中分数阶常微分方程的数值解。该方程的解可以描述反常扩散过程的稳态，该过程源于复杂非均匀背景下的相互作用。我们提出了一种基于有限差分法的数值方法。我们考虑了具有Riesz-Feller分数阶导数的方程边值问题（Dirichlet条件）。在本文的最后部分，展示了一些模拟结果。我们给出了纳米管中非线性温度分布的一个例子，该分布可以通过分数阶微分方程的解来近似。
英文摘要：
In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a steady state of the process of anomalous diffusion. The process arises from interactions within complex and non-homogeneous background. We present a numerical method which is based on the finite differences method. We consider a boundary value problem (Dirichlet conditions) for an equation with the Riesz-Feller fractional derivative. In the final part of this paper, same simulation results are shown. We present an example of non-linear temperature profiles in nanotubes which can be approximated by a solution to the fractional differential equation.
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