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A meshless approach for solving nonlinear variable-order time fractional 2D Ginzburg-Landau equation

机译：一种求解非线性可变阶时间分数2D Ginzburg-Landau方程的无网格方法

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This paper introduces the nonlinear variable-order (VO) time fractional 2D Ginzburg-Landau equation by replacing the conventional derivative with the Atangana-Baleanu-Caputo fractional derivative. An efficient moving least squares (MLS) meshfree approximation method is considered to devise an algorithm for solving this enhanced equation. To be precise, first, the finite difference scheme is used to evaluate the fractional differentiation. Then, a recurrence formula is derived by applying the θ-weighted technique. Next, the real and imaginary components of the solution are expanded in terms of meshless functions. Last, these expansions which include unknown coefficients are input in the original equation. Therefore, the equation is converted into a system of linear algebraic equations which is uncomplicated for solving by mathematical software. To verify the validity of the devised method and demonstrate its precision, several problems are put to the test.
机译：本文介绍了通过用Atangana-Baleanu-Caputo分数衍生物代替常规衍生物来介绍非线性变量（VO）时间分数2D Ginzburg-Landau方程。认为有效的移动最小二乘（MLS）网格映射方法被认为设计了一种求解该增强式方程的算法。要精确，首先，使用有限差分方案来评估分数分化。然后，通过应用θ加权技术来导出复发公式。接下来，解决方案的真实和虚部在无网格函数方面扩展。最后，在原始方程中输入包括未知系数的这些扩展。因此，该等式被转换成线性代数方程的系统，该方程式并不复制，用于通过数学软件解决。要验证设计方法的有效性并展示其精确度，则对测试进行了几个问题。

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