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Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators. (English) Zbl 1176.34096
The authors consider impulsive neutral integro-differential inclusions with nonlocal initial condition and prove the existence of mild solutions. They combine the classic theory of analytic resolvent operators and a fixed point theorem for condensing multivalued maps to obtain the main result. In particular, the sublinear growth case appears naturally as a consequence. A neutral partial integro-differential inclusion with Dirichlet and nonlocal initial condition fulfilling the conditions of the sublinear growth case is presented as an example.

MSC:
34K45 Functional-differential equations with impulses
34K05 General theory of functional-differential equations
45N05 Abstract integral equations, integral equations in abstract spaces
34K30 Functional-differential equations in abstract spaces
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