Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia

IMPACT FACTOR 2018: 3.514
5-year IMPACT FACTOR: 3.524

CiteScore 2018: 3.44

SCImago Journal Rank (SJR) 2018: 1.891
Source Normalized Impact per Paper (SNIP) 2018: 1.808

Mathematical Citation Quotient (MCQ) 2018: 1.08

See all formats and pricing
More options …
Volume 18, Issue 1


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

Aurelian Cernea
  • Corresponding author
  • Faculty of Mathematics and Informatics University of Bucharest Academiei 14, 010014 Bucharest, ROMANIA
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-02-10 | DOI: https://doi.org/10.1515/fca-2015-0011


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


  • [1] A. Aghajani, Y. Jalilian, J. J. Trujillo, On the existence of solutions of fractional integro-differential equations. Fract. Calc. Appl. Anal. 15, No 1 (2012), 44-69; DOI: 10.2478/s13540-012-0005-4; http://link.springer.com/article/10.2478/s13540-012-0005-4.CrossrefGoogle Scholar

  • [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

  • [7] J. Hadamard, Essai sur l'etude des fonctions donnees par leur development de Taylor. J. Math. Pures Appl. 8 (1892), 101-186.Google Scholar

  • [8] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006).Google Scholar

  • [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.

Export Citation

© 2015 Diogenes Co., Sofia.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Bashir Ahmad, Sotiris K. Ntouyas, Yong Zhou, and Ahmed Alsaedi
Bulletin of the Iranian Mathematical Society, 2018
Bashir Ahmad, Sotiris K Ntouyas, Ahmed Alsaedi, and Faris Alzahrani
Boundary Value Problems, 2015, Volume 2015, Number 1

Comments (0)

Please log in or register to comment.
Log in