Sliding-mode boundary control for perturbed time fractional parabolic systems with spatially varying coefficients using backstepping

In this paper, we consider the boundary stabilization of an uncertain time fractional parabolic systems governed by time fractional parabolic partial differential equations (PDEs) with a boundary input disturbance and spatially varying coefficients (nonconstant coefficients) using a fractional-order sliding-mode controller. For this, the backstepping approach is used to transform an original system into a target system with a new manipulable input and perturbation. Then, the fractional-order sliding-mode algorithm is employed to design this new discontinuous boundary input to achieve the asymptotical stabilization of the target system (and, therefore, of the original system as well) by the fractional Lyapunov method. Apart from this, the well-posedness of the fractional parabolic system is analyzed theoretically. Fractional-order numerical simulations are provided to validate the developed technique.