Boundary control of a fractional reaction-diffusion equation coupled with fractional ordinary differential equations with delay

Highlights：

• The system we considered is a fractional reaction-diffusion (FRD) equation with varying coefficient coupled with fractional ordinary differential equations.

• The backstepping method was first applied to control of fractional coupled system with delay.

• A backstepping based boundary feedback control law is designed.

• By an integral transformation, the boundary stabilization problem is converted into a problem of solving a hyperbolic PDE with transformation’s kernel function and a vector-value function.

• The exact solution of target system is given by the Prabhakar function.