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Zbl 1228.45013
Debbouche, Amar; Baleanu, Dumitru
Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. (English)
[J] Comput. Math. Appl. 62, No. 3, 1442-1450 (2011). ISSN 0898-1221

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 2000:: *45K05 Integro-partial differential equations
34A08
34H05 ODE in connection with control problems
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: fractional integro-differential systems; controllability; $(\alpha, u)$-resolvent family; nonlocal and impulsive conditions; fixed point theorem

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