Geodesic
Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces
Zuomao Yan1 ; Hongwu Zhang1
1Department of Mathematics Hexi University Zhangye, Gansu 734000, P.R. China
Annales Polonici Mathematici, Tome 110 (2014) no. 2, pp. 143-169
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap110-2-4
Keywords: study existence mild solutions class impulsive fractional partial neutral integro differential inclusions state dependent delay assume undelayed part generates alpha resolvent operator transform integral equation sufficient conditions existence solutions derived means fixed point theorem discontinuous multi valued operators due dhage properties alpha resolvent operator example given illustrate theory

Zuomao Yan  1   ; Hongwu Zhang  1

1 Department of Mathematics Hexi University Zhangye, Gansu 734000, P.R. China 
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Zuomao Yan; Hongwu Zhang. Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces. Annales Polonici Mathematici, Tome 110 (2014) no. 2, pp. 143-169. doi: 10.4064/ap110-2-4

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