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Relative controllability of linear systems of fractional order with delay. (English) Zbl 1332.93061

Summary: In this paper we are concerned with the controllability of control systems governed by a fractional differential equations with delay. Using the Mittag-Leffler function we define the concept of solution, and applying the properties of the Laplace transform we characterize the relative or pointwise controllability of the system. Our results generalize those of Kirillova and Churakova, which were established for first order systems. Finally, we show that functionally controllable fractional systems are rare.

MSC:

93B05 Controllability
93C23 Control/observation systems governed by functional-differential equations
34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
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