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Approximate controllability of fractional differential equations with state-dependent delay. (English) Zbl 1272.34105
Summary: First, we study the approximate controllability for a class of nonlinear fractional differential equations with state-dependent delays. Then, the result is extended to study the approximate controllability fractional systems with state-dependent delays and resolvent operators. A set of sufficient conditions are established to obtain the required result by employing semigroup theory, fixed point technique and fractional calculus. In particular, the approximate controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is approximately controllable. Also, an example is presented to illustrate the applicability of the obtained theory.

MSC:
34K35 Control problems for functional-differential equations
93B05 Controllability
34K37 Functional-differential equations with fractional derivatives
47N20 Applications of operator theory to differential and integral equations
34K30 Functional-differential equations in abstract spaces
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