Collocation Discrete Least Squares meshless Method for solving Nonlinear Multi-term Time Fractional Differential Equations

Multi-term time fractional equations are designed to give a more accurate and flexible mathematical model for explaining the behavior of physical systems with complex dynamics over time. This model is a generalization of the classical Convection-Diffusion equations (CDEs) which time terms is considered by Caputo's time derivative sense for (0 < ai <= 1, i is an element of N). The meshless method and conjunction with 0-weighted finite difference method are developed for approximating processes in spatial direction. The Moving least squares (MLS) method is a highly effective tool in meshless methods for approximating functions based on scattered data points. It is a versatile and efficient approach that does not rely on a fixed mesh, making it particularly suitable for problems with intricate geometries or data. The proposed method as truly meshless is very promising in numerical approximation of engineering problem within convex, non-convex, irregular and regular domains (complex domains). The reliable and accurate of the proposed method is shown by considering verity computational domain. The sensitivity of the selection of local collocation point and time is reported.