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ArticleOriginal scientific text

Title

Hybrid fractional integro-differential inclusions

Authors 1, 2, 3, 3

Affiliations

  1. Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
  2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
  3. Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Abstract

In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.

Keywords

ENG
fractional differential equations, hybrid differential inclusions, fixed point theorems

Bibliography

  1. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations (North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006).
  2. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley and Sons, New York, 1993).
  3. V. Lakshmikantham, S. Leela and J. Vasundhara Devi, Theory of Fractional Dynamic Systems (Cambridge Academic Publishers, Cambridge, 2009).
  4. V. Lakshmikantham and A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. 69 (8) (2008), 2677-2682. doi: 10.1016/j.na.2007.08.042
  5. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
  6. J. Sabatier, O.P. Agrawal and J.A.T. Machado (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering (Springer, Dordrecht, 2007). doi: 10.1007/978-1-4020-6042-7
  7. B. Ahmad, Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations, Appl. Math. Lett. 23 (2010), 390-394. doi: 10.1016/j.aml.2009.11.004
  8. B. Ahmad and J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58 (2009), 1838-1843. doi: 10.1016/j.camwa.2009.07.091
  9. P. Thiramanus, S.K. Ntouyas and J. Tariboon, Existence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions, Abstr. Appl. Anal. Volume 2014, Article ID 902054, 9 pages.
  10. J. Tariboon, S.K. Ntouyas and W. Sudsutad, Fractional integral problems for fractional differential equations via Caputo derivative, Adv. Differ. Equ. 2014 (2014), 181. doi: 10.1186/1687-1847-2014-181
  11. B. Ahmad, S.K. Ntouyas and A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions, Adv. Differ. Equ. (2011), Art. ID 107384, pp. 11.
  12. B. Ahmad and S.K. Ntouyas, A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order, Electron. J. Qual. Theory Differ. Equ. (2011) No. 22, pp. 15. doi: 10.14232/ejqtde.2011.1.22
  13. B. Ahmad and S. Sivasundaram, Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions, Commun. Appl. Anal. 13 (2009), 121-228.
  14. B. Ahmad and S. Sivasundaram, On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order, Appl. Math. Comput. 217 (2010), 480-487. doi: 10.1016/j.amc.2010.05.080
  15. B. Ahmad, S.K. Ntouyas and A. Alsaedi, Existence theorems for nonlocal multi-valued Hadamard fractional integro-differential boundary value problems, J. Ineq. Appl. 2014 (2014), 454. doi: 10.1186/1029-242X-2014-454
  16. Y. Zhao, S. Sun, Z. Han and Q. Li, Theory of fractional hybrid differential equations, Comput. Math. Appl. 62 (2011), 1312-1324. doi: 10.1016/j.camwa.2011.03.041
  17. S. Sun, Y. Zhao, Z. Han and Y. Li, The existence of solutions for boundary value problem of fractional hybrid differential equations, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 4961-4967. doi: 10.1016/j.cnsns.2012.06.001
  18. B. Ahmad and S.K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal. (2014), Art. ID 705809, 7 pages.
  19. B.C. Dhage and S.K. Ntouyas, Existence results for boundary value problems for fractional hybrid differential inclucions, Topol. Methods Nonlinar Anal. 44 (2014), 229-238.
  20. B. Ahmad, S.K. Ntouyas and A. Alsaedi, Existence results for a system of coupled hybrid fractional differential equations, The Scientific World Journal, Volume 2014, Article ID 426438, 6 pages.
  21. B. Ahmad and S.K. Ntouyas, An existence theorem for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions, Abstr. Appl. Anal. 2014 (2014), Article ID 705809, 7 pages.
  22. B.C. Dhage, A fixed point theorem in Banach algebras with applications to functional integral equations, Kyungpook Math. J. 44 (2004), 145-155.
  23. S. Sitho, S.K. Ntouyas and J. Tariboon, Existence results for hybrid fractional integro-differential equations, Bound. Value Prob. 2015 (2015), 113. doi: 10.1186/s13661-015-0376-7
  24. A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2015/35/2
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Pages:
151-164
Main language of publication
English
Received
2015-09-24
Published
2015

DOI: 10.7151/dmdico.1174

Exact and natural sciences