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2012 | 32 | 1 | 45-62
Tytuł artykułu

Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.
Twórcy
autor
  • Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
  • Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Bibliografia
  • [1] B. Ahmad, A. Alsaedi and B. Alghamdi, Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, Nonlinear Anal. Real World Appl. 9 (2008) 1727-1740. doi: 10.1016/j.nonrwa.2007.05.005
  • [2] B. Ahmad and J.J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. Value Probl. 2009, Art. ID 708576, 11 pp.
  • [3] B. Ahmad and V. Otero-Espinar, Existence of solutions for fractional differential inclusions with anti-periodic boundary conditions, Bound. Value Probl. 2009 (2009), Article ID 625347, 11 pages.
  • [4] B. Ahmad and S. Sivasundaram, Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Anal. Hybrid Syst. 4 (2010) 134-141. doi: 10.1016/j.nahs.2009.09.002
  • [5] B. Ahmad and J.J. Nieto, Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory, Topological Methods in Nonlinear Analysis 35 (2010) 295-304.
  • [6] B. Ahmad, S.K. Ntouyas and A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions, Adv. Difference Equ. 2011, Art. ID 107384, 11 pp.
  • [7] B. Ahmad, J. Nieto and A. Alsaedi, Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions, Acta Math. Scientia 31B (2011) 2122-2130. doi: 10.1016/S0252-9602(11)60388-3
  • [8] M. Benchohra, John R. Graef and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal. 87 (2008) 851-863.
  • [9] A. Boucherif, Second-order boundary value problems with integral boundary conditions, Nonlinear Anal. 70 (2009) 364-371. doi: 10.1016/j.na.2007.12.007
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  • [13] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
  • [14]S. Hamani, M. Benchohra and John R. Graef, Existence results for boundary value problems with nonlinear fractional inclusions and integral conditions, Electronic J. Differential Equations 2010 (20) (2010) 1-16.
  • [15] 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.
  • [16] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991.
  • [17] 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. Math. 13 (1965) 781-786.
  • [18] X. Liu, M. Jia and B. Wu, Existence and uniqueness of solution for fractional differential equations with integral boundary conditions, E.J. Qualitative Theory of Diff. Equ. 69 (2009) 1-10.
  • [19] H.A.H. Salem, Fractional order boundary value problem with integral boundary conditions involving Pettis integral, Acta Math. Scientia 31 (2011) 661-672. doi: 10.1016/S0252-9602(11)60266-X
  • [20] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1137
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