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2015 | 35 | 2 | 151-164
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Hybrid fractional integro-differential inclusions

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EN
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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.
Twórcy
  • Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
  • 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
  • Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
  • Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
Bibliografia
  • [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).
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  • [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.
Typ dokumentu
Bibliografia
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