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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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Mathematical Citation Quotient (MCQ) 2018: 0.62

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Existence results for fractional integro-differential inclusions with state-dependent delay

Giovana Siracusa
  • Departamento de Matemática, Universidade Federal de Sergipe, Cidade Universitária Prof. Aloísio Campos, São Cristóvão-SE, CEP 49100-00, Brazil
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/ Hernán R. Henríquez / Claudio Cuevas
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  • Departamento de Matemática, Universidade Federal de Pernambuco, Av. Jornalista Anibal Fernandez, s/n, Recife-PE, CEP 50540-740, Brazil
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Published Online: 2017-10-25 | DOI: https://doi.org/10.1515/msds-2017-0007


In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

Keywords : Fractional integral-differential inclusion; Multi-valued maps; Resolvent Operator; State-dependent delay

MSC 2010: Primary 34K37; 34G25. Secondary 34K30; 34K09


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About the article

Received: 2017-03-13

Accepted: 2017-09-25

Published Online: 2017-10-25

Published in Print: 2017-10-26

Citation Information: Nonautonomous Dynamical Systems, Volume 4, Issue 1, Pages 62–77, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2017-0007.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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