The method of approximate particular solutions to simulate an anomalous mobile‐immobile transport process

In the current work, a generalized mathematical model based on the Coimbra time fractional derivative of variable order, which describes an anomalous mobile‐immobile transport process in complex systems is investigated numerically. A robust numerical technique based on the meshfree strong form method combined with an efficient time‐stepping scheme is performed to compute the approximate solution of the problem with high accuracy. For this purpose, firstly, an effective implicit time discretization approach is used for discretizing the variable‐order time fractional problem in the time direction. Then a global meshless technique based on the method of approximate particular solutions is performed to fully discretize the model in the spatial domain. The validity and performance of the procedure to numerically simulate the proposed generalized solute transport model on regular and irregular domains are demonstrated through some numerical examples.