Stability of fractional order parabolic partial differential equations using discretised backstepping method

This paper focuses on the application of backstepping control scheme for fractional order partial differential equations (FPDEs) of order with . Therefore to obtain highly accurate approximations for this derivative is of great importance. Here the discretised approach for the space variable is used to transform the FPDEs into a system of differential equations. These approximations arise mainly from the Caputo definition and the Grünwald-Letnikov definition. A Lyapunov function is defined at each stage and the negativity of an overall Lyapunov function is ensured by proper selection of the control law. Illustrative example is given to demonstrate the effectiveness of the proposed control scheme.