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Fractional BDF methods for solving fractional differential matrix equations. (English) Zbl 1515.65095

Summary: 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 \(\beta\), 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.

MSC:

65F45 Numerical methods for matrix equations
15A24 Matrix equations and identities
34A08 Fractional ordinary differential equations
65R20 Numerical methods for integral equations
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