Yan, Zuomao; Zhang, Hongwu Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces. (English) Zbl 1382.34076 Ann. Pol. Math. 110, No. 2, 143-169 (2014). 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. Cited in 2 Documents 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 Keywords:impulsive integro-differential inclusions; fractional partial neutral integro-differential inclusions; multi-valued map; state-dependent delay; \(\alpha \)-resolvent operator PDFBibTeX XMLCite \textit{Z. Yan} and \textit{H. Zhang}, Ann. Pol. Math. 110, No. 2, 143--169 (2014; Zbl 1382.34076) Full Text: DOI