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Controllability of neutral fractional functional equations with impulses and infinite delay. (English) Zbl 1421.93020

Summary: We examine the controllability problem for a class of neutral fractional integrodifferential equations with impulses and infinite delay. More precisely, a set of sufficient conditions are derived for the exact controllability of nonlinear neutral impulsive fractional functional equation with infinite delay. Further, as a corollary, approximate controllability result is discussed by assuming compactness conditions on solution operator. The results are established by using solution operator, fractional calculations, and fixed point techniques. In particular, the controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is controllable. Finally, an example is given to illustrate the obtained theory.

MSC:

93B05 Controllability
34A08 Fractional ordinary differential equations
93C23 Control/observation systems governed by functional-differential equations
34K37 Functional-differential equations with fractional derivatives
93E03 Stochastic systems in control theory (general)
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