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Fractional Calculus and Applied Analysis

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Volume 20, Issue 6

On generalized boundary value problems for a class of fractional differential inclusions

Irene Benedetti / Valeri Obukhovskii
  • Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 Voronezh, Russia
  • The RUDN University, 117198 Moscow, Russia
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/ Valentina Taddei
  • Dipartimento di Scienze e Metodi per l’Ingegneria, Università di Modena e Reggio Emilia, I–42122 Reggio Emilia, Italy
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Published Online: 2017-12-29 | DOI: https://doi.org/10.1515/fca-2017-0075

Abstract

We prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-differential inclusions.

MSC 2010: Primary 34A08; 34G20; 34B10; Secondary 54C60; 35K91; 54C08

Key Words and Phrases: nonlocal conditions; fixed point theorem; fractional derivative

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About the article

Received: 2017-04-30

Published Online: 2017-12-29

Published in Print: 2017-12-20


Citation Information: Fractional Calculus and Applied Analysis, Volume 20, Issue 6, Pages 1424–1446, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2017-0075.

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