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This paper is concerned with the controllability of higher order fractional damped delay dynamical systems with time varying multiple delays in control, which involved Caputo derivatives of any di erent orders. A necessary and su cient condition for the controllability of linear fractional damped delay dynamical system is obtained by using the Grammian matrix. Su cient conditions for controllability of the corresponding nonlinear damped delay dynamical system has established by the successive approximation technique. Examples have provided to verify the results.

Controllability of Higher Order Fractional Damped Delay Dynamical Systems with Time Varying Multiple Delays in Control