In this work, a radial basis function (RBF)-based numerical scheme is developed which uses the Coimbra variable time fractional derivative of order \(0<\alpha (t,x)< 1\). The Coimbra derivative can efficiently model a dynamical system whose fractional-order behavior changes with time and space locations. The RBF can effectively approximate spatial derivatives in multi-dimensions. The resulted numerical scheme is RBF–FD type and is validated for solute transport problems in 1D and 2D dimension domains. Various cases of variable-order \(0<\alpha (t,x)< 1\) have been discussed. The present numerical scheme can effectively approximate those variable-order models whose exact solution can not be obtained in a simple way.

在这项工作中，开发了一种基于径向基函数（RBF）的数值方案，该方案使用了\（0 <\ alpha（t，x）<1 \）阶的Coimbra可变时间分数导数。Coimbra导数可以有效地建模其分数阶行为随时间和空间位置而变化的动力学系统。RBF可以有效地近似多维的空间导数。所得的数值方案为RBF–FD型，并针对一维和二维维域中的溶质输运问题进行了验证。讨论了可变阶\（0 <\ alpha（t，x）<1 \）的各种情况。本数值方案可以有效地近似那些无法以简单方式获得精确解的变量阶模型。