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# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces

### Tom 110 / 2014

Annales Polonici Mathematici 110 (2014), 143-169 MSC: Primary 34A37, 34A60; Secondary 35R12, 26A33. DOI: 10.4064/ap110-2-4

#### Streszczenie

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.

#### Autorzy

• Zuomao YanDepartment of Mathematics
Hexi University
Zhangye, Gansu 734000, P.R. China
e-mail
• Hongwu ZhangDepartment of Mathematics
Hexi University
Zhangye, Gansu 734000, P.R. China

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