A study of an efficient numerical method for solving the generalized fractional reaction-diffusion model involving a distributed-order operator along with stability analysis

In this manuscript, we study a generalized fractional reaction-diffusion model involving a distributed-order operator. An efficient hybrid approach is proposed to solve the presented model. The L1 approximation is utilized to discretize the time variable, while the mixed finite element method is employed for spatial discretization. A detailed error and stability analysis of the proposed method is provided. Furthermore, we prove that the computational accuracy achieved by the proposed approach is of order O(h2+(Δt)3−ξmax). To validate and evaluate the numerical approach, three numerical experiments are conducted, with results presented through graphs and tables.