A local meshless numerical scheme based on the radial point interpolation forthegeneralizedtime-fractionalAllen-Cahnequation

This research has been conducted to investigate a numerical solution for the Allen-Cahn equation featuring the generalized fractional time derivative. The finite difference method is employed to discretize the equation in the time variable. Subsequently, an error estimate is derived for the proposed method in L-p,L-mu,L-q space. Furthermore, a meshless technique based on radial point interpolation is used to discretize the problem in spatial variables. Through these procedures, the equation is transformed into a system of linear equations at each time step. The method's effectiveness for solving this equation is demonstrated by three examples on both regular and irregular domains. These examples illustrate that the current method has a high level of accuracy and efficiency for solving the given problem.