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Tytuł artykułu

Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

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Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
Twórcy
  • Département de Mathématiques, Université de Ghardaia, Algérie
  • Département de Mathématiques, Université de Ghardaia, Algérie
  • Laboratoire de Mathématiques, Université de Sidi Bel Abbès, Algérie
autor
  • Département de Mathématiques, E.N.S Constantine, Algérie
Bibliografia
  • [1] S. Abbas, M. Benchohra and G.M. N'Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012. doi: 10.1007/978-1-4614-4036-9
  • [2] R.P. Agarwal, M. Benchohra and S. Hamani, Boundary value problems for fractional differential equations, Adv. Stud. Contemp. Math. 16 (2008), 181-196.
  • [3] A. Anguraj, P. Karthikeyan and G.M. N'Guérékata, Nonlocal Cauchy problem for some fractional abstract differential equations in Banach spaces, Commun. Math. Anal. 6 (2009).
  • [4] D. Baleanu, K. Diethelm, E. Scalas and J.J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York, 2012.
  • [5] M. Belmekki and M. Benchohra, Existence results for fractional order semilinear functional differential equations, Proc. A. Razmadze Math. Inst. 146 (2008), 9-20.
  • [6] M. Belmekki, M. Benchohra and L. Górniewicz, Semilinear functional differential equations with fractional order and infinite delay, Fixed Point Th. 9 (2008), 423-439.
  • [7] M. Benchohra, J.R. Graef and S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal. 87 (2008), 851-863. doi: 10.1080/00036810802307579
  • [8] M. Benchohra, J. Henderson, S.K. Ntouyas and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008), 1340-1350. doi: 10.1016/j.jmaa.2007.06.021
  • [9] M. Benchohra, S. Litimein and G. N'Guérékata, On fractional integro-differential inclusions with state-dependent delay in Banach spaces, Appl. Anal. 92 (2013), 335-350. doi: 10.1080/00036811.2011.616496
  • [10] C. Chen and M. Li, On fractional resolvent operator functions Semigroup Forum. 80 (2010), 121-142. doi: 10.1007/s00233-009-9184-7
  • [11] C-Cuevas and J-C. de Souza, S-asymptotically W-periodic solutions of semilinear fractional integro-differential equations, Appl. Math. Lett. 22 (2009), 865-870. doi: 10.1016/j.aml.2008.07.013
  • [12] C-Cuevas and J-C. de Souza, Existence of S-asymptotically W-periodic solutions of fractional order functional integro-differential equations with infinite delay, Nonlinear Anal. 72 (2010), 1680-1689. doi: 10.1016/j.na.2009.09.007
  • [13] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003. doi: 10.1007/978-0-387-21593-8
  • [14] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [15] A.A. Kilbas, Hari M. Srivastava and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
  • [16] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
  • [17] A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
  • [18] M. Li and Q. Zheng, On spectral inclusions and approximations of α-times resolvent families, Semigroup Forum. 69 (2004), 356-368.
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  • [22] V.E. Tarasov, Fractional Dynamics. Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg, 2010.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1149
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