Using the meshless collocation method, a scheme for solving nonlinear variable-order fractional diffusion equations with a fourth-order derivative term is presented. Here the fractional derivative term is approximated by weighted and shifted Grünwald difference (WSGD) approximation formula. The difficulty caused by the nonlinear terms is carefully handled by quasilinearization technique. Using the radial basis functions, the solution of the problem is written in terms of the primary approximation, and the related correcting functions at each time step. Then the approximation is substituted back to the governing equations where the unknown parameters can be determined. Finally, the method is supported by several numerical experiments on irregular domains.

利用无网格配置方法，提出了一种求解具有四阶导数项的非线性变阶分数扩散方程的方案。在这里，分数导数项通过加权和移位的 Grünwald 差分 (WSGD) 近似公式来近似。由非线性项引起的困难通过准线性化技术仔细处理。使用径向基函数，问题的解决方案是根据初级近似和每个时间步的相关校正函数来编写的。然后将近似值代入可以确定未知参数的控制方程。最后，该方法得到了不规则域上的几个数值实验的支持。