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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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