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Relative controllability of fractional dynamical systems with delays in control. (English) Zbl 1248.93022

Summary: This paper is concerned with the controllability of nonlinear fractional dynamical systems with time varying multiple delays and distributed delays in control defined in finite dimensional spaces. Sufficient conditions for controllability results are obtained using Schauder’s fixed-point theorem and the controllability Gramian matrix which is defined by using the Mittag–Leffler matrix function. Examples are provided to illustrate the theory.

MSC:

93B05 Controllability
34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
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