Synchronization of Distributed Fractional-Order Nonlinear Dynamical Systems

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We provide an approach for designing dynamical distributed controllers for the synchronisation problem of systems governed by integer and fractional order partial differential equations in this paper. We analyse fractional systems with integer order space derivatives and fractional commensurate order temporal derivatives. The methodology is based on the discovery of canonical forms via a variable change, allowing a distributed controller to be developed naturally in the form of a chain of integrators. We propose to employ spectral and semigroup theory for infinite dimensional Hilbert spaces to investigate the stability of the integer order closed loop system