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On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces

100%
Yan Z.
Annales Polonici Mathematici
|
2011
|
tom 101
|
nr 1
87-103
EN
This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by using strongly continuous operator semigroups and Bohnenblust-Karlin's fixed point theorem.
2
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Existence results for fractional functional integrodifferential equations with nonlocal conditions in Banach spaces

100%
Yan Z.
Annales Polonici Mathematici
|
2010
|
tom 97
|
nr 3
285-299
EN
The paper establishes a sufficient condition for the existence of mild solutions of fractional functional integrodifferential equations with nonlocal conditions in Banach spaces. Our approach is based on Schaefer's fixed point theorem combined with the use of strongly continuous operator semigroups. As an application, we also consider a fractional partial functional integrodifferential equation.
3
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Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces

63%
Yan Z., Zhang H.
Annales Polonici Mathematici
|
2014
|
tom 110
|
nr 2
143-169
EN
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 α-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 α-resolvent operator. An example is given to illustrate the theory.
4
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Stepanov-like square-mean pseudo almost automorphic solutions to partial neutral stochastic functional differential equations

51%
Yan Z., Jia X.-M., Yan X.
Annales Polonici Mathematici
|
2013
|
tom 108
|
nr 3
263-287
EN
We obtain the existence and uniqueness of square-mean pseudo almost automorphic mild solutions to first-order partial neutral stochastic functional differential equations with Stepanov-like almost automorphic coefficients in a real separable Hilbert space.
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