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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:
34K35Functional-differential equations connected with control problems
93B05Controllability
34K37Functional-differential equations with fractional derivatives
47N20Applications of operator theory to differential and integral equations
34K30Functional-differential equations in abstract spaces
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