An efficient and optimal numerical approach for solving a time-fractional fourth-order reaction-diffusion model with a distributed-order operator on complex domains

This paper presents an efficient numerical approach for solving the time-fractional fourth-order reaction-diffusion model involving a distributed-order operator. To discretize the fractional Caputo operator in time, quadratic and linear interpolation approximations are applied. For spatial discretization of the derivative operator, a direct meshless local Petrov-Galerkin scheme is used on the computational domain, which includes complex shapes. Stability and convergence analyses of the proposed numerical approach are presented and discussed. To evaluate the efficiency and performance of the method, several numerical examples are provided. Charts and tables are included to better illustrate the accuracy of the proposed method.