In this paper, we have developed an radial basis function (RBF) based meshless method to solve the time-fractional mixed diffusion and diffusion-wave equation which involves two fractional Caputo derivatives of order α∈(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (0,1)$$\end{document} and β∈(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta \in (1,2)$$\end{document}. The unconditional stability of the proposed numerical scheme is discussed and proved theoretically. The time semi discretization has been done by using the finite difference method and for space discretization, we proposed an RBF-based local collocation method. Some test problems are considered for regular as well as an irregular domain with uniform and non-uniform points to validate the efficiency and accuracy of the method.

中文翻译：

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基于RBF的无网格法求解时分混合扩散和扩散波方程

在本文中，我们开发了一种基于径向基函数 (RBF) 的无网格方法来求解时间分数混合扩散和扩散波方程，该方程涉及阶次为 α∈(0,1)\documentclass[12pt] 的两个分数 Caputo 导数{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin {document}$$\alpha \in (0,1)$$\end{document} 和 β∈(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{ amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta \in (1,2)$$ \end{文档}。讨论并理论上证明了所提出的数值方案的无条件稳定性。采用有限差分法进行时间半离散化，对于空间离散化，我们提出了一种基于RBF的局部搭配方法。一些测试问题被考虑用于具有均匀和非均匀点的规则域和不规则域，以验证该方法的效率和准确性。