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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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Volume 18, Issue 1

Issues

Filippov Lemma for a Class of Hadamard-Type Fractional Differential Inclusions

Aurelian Cernea
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  • Faculty of Mathematics and Informatics University of Bucharest Academiei 14, 010014 Bucharest, ROMANIA
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Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0011

Abstract

We study a class of fractional integro-differential inclusions with integral boundary conditions and establish a Filippov type existence result in the case of nonconvex set-valued maps.

MSC 2010: Primary 34A60; Secondary 34A08

Key Words and Phrases: differential inclusion; fractional derivative; boundary value problem

References

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  • [2] B. Ahmad, S. K. Ntouyas, Fractional differential inclusions with fractional separated boundary conditions. Fract. Calc. Appl. Anal. 15, No 3 (2012), 362-382; DOI: 10.2478/s13540-012-0027-y; http://link.springer.com/article/10.2478/s13540-012-0027-y.CrossrefGoogle Scholar

  • [3] B. Ahmad, S. K. Ntouyas, A. Alsaedi, New results for boundary value problems of Hadamard-type fractional differential inclusions and integral boundary conditions. Boundary Value Problems 2013 (2013), Paper No 275, 14 p.Google Scholar

  • [4] B. Ahmad, S. K. Ntouyas, A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations. Fract. Calc. Appl. Anal. 17, No 2 (2014), 348-360; DOI: 10.2478/s13540-014-0173-5; http://link.springer.com/article/10.2478/s13540-014-0173-5.CrossrefGoogle Scholar

  • [5] J. P. Aubin, H. Frankowska, Set-valued Analysis. Birkhauser, Basel (1990).Google Scholar

  • [6] A. F. Filippov, Classical solutions of differential equations with multivalued right hand side. SIAM J. Control 5 (1967), 609-621.CrossrefGoogle Scholar

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  • [9] A. A. Kilbas, Hadamard-type fractional calculus. J. Korean Math. Soc. 38 (2001), 1191-1204.Google Scholar

About the article

Received: 2014-06-05

Published Online: 2015-02-10


Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 1, Pages 163–171, ISSN (Online) 1314-2224, DOI: https://doi.org/10.1515/fca-2015-0011.

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