Fractional BDF Methods for Solving Fractional Differential Matrix Equations

In this paper, fractional backward differentiation formulas methods (FBDF) of the order r are presented for the numerical solution of fractional differential matrix equations (FD-MEs) in Caputo sense of fractional order β, for example, Sylvester, Lyapunov, Riccati, and Stein for the first time. The approach is constituted of the Grünwald approximation and the matrix operations and solving a matrix equation for each step. The error analysis and the convergence have been presented. Finally, some attractive and interesting examples of specific problems are considered and solved to illustrate the effectiveness of the proposed framework, several different numerical examples are given to show the effectiveness of the methods. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.