An Efficient Numerical Approach for Solving Time-Space Fractional Wave Model of Multiterm Order Involving the Riesz Fractional Operators of Distributed Order With the Weakly Singular Kernel Along With Stability Analysis

In this manuscript, we propose an efficient numerical approach to solve the time-space fractional wave model of multiterm order, incorporating Riesz fractional operators of distributed order with a weakly singular kernel. The approach combines numerical techniques to approximate the model in both the spatial and temporal directions. For the time variable, the $L1$ approximation is employed, while a second-order accurate fractional-centered difference method is used for the spatial variable. We provide a detailed stability and convergence analysis for the fully discrete numerical scheme. To demonstrate the accuracy and efficiency of the proposed method, we present and simulate two numerical examples. The results of these examples are displayed graphically to illustrate the effectiveness of the approach.