부산대학교 도서관

Summary: ``This paper addresses a boundary state feedback control problem for a coupled system of time fractional partial differential equations (PDEs) with non-constant (space-dependent) coefficients and different-type boundary conditions (BCs). The BCs could be heterogeneous-type or mixed-type. Specifically, this coupled system has different BCs at the uncontrolled side for heterogeneous-type and the same BCs at the uncontrolled side for mixed-type. The main contribution is to extend PDE back- stepping to the boundary control problem of time fractional PDEs with space-dependent parameters and different-type BCs. With the backstepping transformation and the fractional Lyapunov method, the Mittag-Leffler stability of the closed-loop system is obtained. A numerical scheme is proposed to simulate the fractional case when kernel equations have not an explicit solution.'' \par This paper uses a backstepping approach to study a boundary feedback control problem for a system of time-fractional diffusion equations. A numerical scheme to approximate the system is also proposed.