THE METHODS OF FRACTIONAL BACKWARD DIFFERENTIATION FORMULAS FOR SOLVING TWO-TERM FRACTIONAL DIFFERENTIAL SYLVESTER MATRIX EQUATIONS

In this paper, we present the fractional backward differentiation formulas for the numerical solutions of two-term fractional differential Sylvester matrix equations in the Caputo derivative sense, which includes the celebrated two-term fractional differential Lyapunov matrix equations. We give two applications in a two-term time-fractional telegraph equation with illustrative examples. In addition, we also consider two examples to illustrate the effectiveness of the proposed approaches. ©2024 Applied Set-Valued Analysis and Optimization.