ArticleOriginal scientific text

Title

On a partial Hadamard fractional integral inclusion

Authors 1

Affiliations

  1. Faculty of Mathematics and Computer Science University of Bucharest Academy of Romanian Scientists Splaiul Independent¸ei 54, 050094 Bucharest, Romania

Abstract

We study a class of nonconvex Hadamard fractional integral inclusions and we establish some Filippov type existence results.

Keywords

Hadamard fractional derivative, integral inclusion, decomposable set

Bibliography

  1. S. Abbas, E. Alaidarous, W. Albarakati and M. Benchohra, Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions, Discuss. Math. DICO 35 (2015), 105-122. doi: 10.7151/dmdico.1172
  2. S. Abbas, W. Albarakati, M. Benchohra and J. Henderson, Existence and Ulam stabilities for Hadamard fractional integral equations with random effects, Electronic J. Diff. Equations 2016 (2016), 1-12.
  3. S. Abbas, M. Benchohra and J. Henderson, Partial Hadamard fractional integral equations, Adv. Dynam. Systems Appl 10 (2015), 97-107.
  4. D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional Calculus: Models and Numerical Methods, World Scientific, Singapore, 2012, 10.1142/8180.
  5. A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math 90 (1988), 69-86.
  6. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions (Springer, Berlin,1977). doi: 10.1007/BFb0087685
  7. A. Cernea, On the existence of solutions for nonconvex fractional hyperbolic differential inclusions, Commun. Math. Analysis 9 (2010), 109-120.
  8. A. Cernea, On an integro-differential inclusion of fractional order, Diff. Equations Dynam. Systems 21 (2013), 225-236. doi: 10.1007/s12591-012-0148-0
  9. A. Cernea, Filippov lemma for a class of Hadamard-type fractional differential inclusions, Fractional Calculus Appl. Analysis 18 (2015), 163-171. doi: 10.1515/fca-2015-0011
  10. A.F. Filippov, Classical solutions of differential equations with multivalued right hand side, SIAM J. Control 5 (1967), 609-621. doi: 10.1137/0305040
  11. J. Hadamard, Essai sur l'etude des fonctions donnees par leur development de Taylor, J. Math. Pures Appl. 8 (1892), 101-186.
  12. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006).
  13. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc. 38 (2001), 1191-1204.
  14. M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht, 1991).
  15. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
Pages:
141-153
Main language of publication
English
Received
2016-09-06
Published
2016
Exact and natural sciences