This study deals with obtaining numerical solutions of two‐dimensional (2D) fractional cable equation in neuronal dynamics by using a recently introduced meshless method. In solution process at first stage, time derivatives that are appeared in the considered problem are discretized by using finite difference method. Then a meshless method based on hybridization of Gaussian and cubic kernels is developed in local fashion. The problem is solved both on regular and irregular domians. L_∞ and RMS error norms are calculated and compared with other numerical methods in literature as well as exact solutions. Also, obtained condition numbers are monitored. Numerical simulations show that local hybrid kernel meshless method is a thriving method for solving 2D fractional cable equation on regular and irregular domians.

中文翻译：

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神经元动力学中二维分数线方程数值解的局部混合核无网格方法

这项研究致力于通过使用最近引入的无网格方法获得神经元动力学中二维（2D）分数电缆方程的数值解。在第一阶段的求解过程中，使用有限差分法离散考虑问题中出现的时间导数。然后以局部方式发展了基于高斯和立方核混合的无网格方法。定期和不定期的domian问题都可以解决。大号_∞和RMS计算误差范数，并将其与文献中的其他数值方法以及精确解进行比较。另外，监视获得的条件编号。数值模拟表明，局部混合核无网格法是求解规则和不规则domian上的二维分数线方程的一种兴旺方法。