一种基于Chebyshev小波的新方法用于变阶时间分数移动-不移动对流-扩散模型
A new approach of the Chebyshev wavelets for the variable-order time fractional mobile-immobile advection-dispersion model
AI总结：
本文提出了一种基于Chebyshev小波的新数值方法，用于求解变阶时间分数移动-不移动对流-扩散方程。通过推导新的变阶分数导数运算矩阵，将问题转化为线性代数方程组，从而高效准确地获得近似解。
摘要：
本文提出了一种基于Chebyshev小波的新数值方法，用于求解变阶时间分数移动-不移动对流-扩散方程。为此，推导了基于Chebyshev小波的新的变阶分数导数运算矩阵，并用于获得所研究问题的近似解。在此过程中引入了一种新的分段函数族，并用于推导计算该矩阵的一般方法。所提出方法的主要优势是将所考虑的问题转化为线性代数方程组，从而可以简单求解以获得近似解。通过一些具体例子展示了所提方法的效率和精度。这些结果表明，所提出的方法非常高效和准确。
英文摘要：
This paper proposes a new numerical method based on the Chebyshev wavelets (CWs) to solve the variable-order time fractional mobile-immobile advection-dispersion equation. To do this, a new operational matrix of variable-order fractional derivative in the Caputo sense for the CWs is derived and is used to obtain an approximate solution for the problem under study. Along the way a new family of piecewise functions is introduced and employed to derive a general method to compute this matrix. The main advantage behind the proposed approach is that the problem under consideration is transformed into a linear system of algebraic equations. So, it can be solved simply to obtain an approximate solution. The efficiency and accuracy of the proposed method are shown for some concrete examples. These results show that the proposed method is very efficient and accurate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
