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Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. (English) Zbl 1228.45013
Summary: A controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems in a Banach space has been established by using the theory of fractional calculus, fixed point technique and also we introduced a new concept called $$(\alpha ,u)$$-resolvent family. As an application that illustrates the abstract results, an example is given.

##### MSC:
 45K05 Integro-partial differential equations 34A08 Fractional ordinary differential equations 34H05 Control problems involving ordinary differential equations 47H10 Fixed-point theorems
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