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2013 | 33 | 1 | 17-39
Tytuł artykułu

Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions

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EN
Abstrakty
EN
This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.
Twórcy
  • Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Bibliografia
  • [1] R.P. Agarwal, B. Andrade and C. Cuevas, Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Nonlinear Anal. Real World Appl. 11 (2010) 3532-3554. doi: 10.1016/j.nonrwa.2010.01.002
  • [2] 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
  • [3] B. Ahmad, T. Hayat and S. Asghar, Diffraction of a plane wave by an elastic knife-edge adjacent to a strip, Canad. Appl. Math. Quart. 9 (2001) 303-316.
  • [4] B. Ahmad and S.K. Ntouyas, Existence results for nonlinear fractional differential equations with four-point nonlocal type integral boundary conditions, Afr. Diaspora J. Math. 11 (2011) 29-39.
  • [5] B. Ahmad and S.K. Ntouyas, Some existence results for boundary value problems for fractional differential inclusions with non-separated boundary conditions, Electron. J. Qual. Theory Differ. Equ. 71 (2010) 1-17. doi: 10.1155/2010/279493
  • [6] 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
  • [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 of solutions for nonlocal boundary value problems of higher order nonlinear fractional differential equations, Abstr. Appl. Anal., (2009), Article ID 494720, 9 pages.
  • [9] 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.
  • [10] 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
  • [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., Volume 2011, Article ID 107384, 11 pages.
  • [12] S. Asghar, B. Ahmad and M. Ayub, Diffraction from an absorbing half plane due to a finite cylindrical source, Acustica-Acta Acustica 82 (1996) 365-367.
  • [13] Z.B. Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal. 72 (2010) 916-924. doi: 10.1016/j.na.2009.07.033
  • [14] K. Balachandran and J. J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear Anal. 72 (2010) 4587-4593. doi: 10.1016/j.na.2010.02.035
  • [15] D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional calculus models and numerical methods. Series on Complexity, Nonlinearity and Chaos (World Scientific, Boston, 2012).
  • [16] D. Baleanu and O.G. Mustafa, On the global existence of solutions to a class of fractional differential equations, Comp. Math. Appl. 59 (2010) 1835-1841. doi: 10.1016/j.camwa.2009.08.028
  • [17] D. Baleanu, O.G. Mustafa and D. O'Regan, A Nagumo-like uniqueness theorem for fractional differential equations, J. Phys. A, Math. Theor. 44 (39) (2011) 6 p. Article ID 392003.
  • [18] 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
  • [19] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988) 69-86.
  • [20] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580 (Springer-Verlag, Berlin-Heidelberg-New York, 1977). doi: 10.1007/BFb0087685
  • [21] H. Covitz and S.B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970) 5-11. doi: 10.1007/BF02771543
  • [22] K. Deimling, Multivalued Differential Equations (Walter De Gruyter, Berlin-New York, 1992). doi: 10.1515/9783110874228
  • [23] M. Frigon, Théorèmes d'existence de solutions d'inclusions différentielles, Topological Methods in Differential Equations and Inclusions (edited by A. Granas and M. Frigon), NATO ASI Series C, Vol. 472, Kluwer Acad. Publ. (Dordrecht, 1995) 51-87.
  • [24] A. Granas and J. Dugundji, Fixed Point Theory (Springer-Verlag, New York, 2005).
  • [25] A. Guezane-Lakoud and R. Khaldi, Solvability of a fractional boundary value problem with fractional integral condition, Nonlinear Anal. 75 (2012) 2692-2700. doi: 10.1016/j.na.2011.11.014
  • [26] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Theory I (Kluwer, Dordrecht, 1997).
  • [27] 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).
  • [28] M.A. Krasnoselskii, Two remarks on the method of successive approximations, Uspekhi Mat. Nauk 10 (1955) 123-127.
  • [29] M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht, The Netherlands, 1991).
  • [30] 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.
  • [31] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
  • [32] 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_1146
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