Boundary fractional derivative control of the wave equation

The wave equation, with fractional derivative feedback at the boundary, is studied. The existence and uniqueness, as well as the asymptotic decay of the solution towards zero is proved. The method used is motivated by the fact that the input-output relationship as generalized diffusion equations, defined on the infinite spatial domain R with collocated sensor and actuator control, can be expressed in terms of fractional integrals. Compared to other methods, the payoff is as follows: 1) the proofs are simpler; and 2) the method used can easily be adapted to a wide class of problems involving fractional derivative or integral operators of the time variable.>