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Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces. (English) Zbl 1382.34076

Summary: We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an \(\alpha \)-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the \(\alpha \)-resolvent operator. An example is given to illustrate the theory.

MSC:

34K30 Functional-differential equations in abstract spaces
34K09 Functional-differential inclusions
34K45 Functional-differential equations with impulses
34K37 Functional-differential equations with fractional derivatives
35R12 Impulsive partial differential equations
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