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Fractional order impulsive partial hyperbolic differential inclusions with variable times

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EN
This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
Twórcy
autor
  • Laboratoire de Mathématiques, Université de Saïda, B.P. 138, 20000, Saïda, Algérie
  • Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, B.P. 89, 22000, Sidi Bel-Abbès, Algérie
  • Institute of Mathematics, Kazimierz Wielki University, Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
  • J. Schauder Center for Nonlinear Studies, University of Nicolaus Copernicus, 87-100 Toruń, Poland
Bibliografia
  • [1] S. Abbas and M. Benchohra, Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative, Commun. Math. Anal. 7 (2009), 62-72.
  • [2] S. Abbas and M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay, Nonlinear Anal. Hybrid Syst. 3 (2009), 597-604. doi: 10.1016/j.nahs9.05.001.200
  • [3] S. Abbas and M. Benchohra, Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order, Nonlinear Anal. Hybrid Syst. 4 (2010), 406-413. doi: 10.1016/j.nahs.2009.10.004
  • [4] S. Abbas and M. Benchohra, The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses, Discuss. Math. Differ. Incl. Control Optim. 30 (1) (2010), 141-161. empty
  • [5] S. Abbas and M. Benchohra, Existence theory for impulsive partial hyperbolic differential equations of fractional order at variable times, Fixed Point Theory, (to appear).
  • [6] S. Abbas, M. Benchohra and L. Górniewicz, Existence theory for impulsive partial hyperbolic functional differential equations involving the Caputo fractional derivative, Sci. Math. Jpn. online e- 2010, 271-282.
  • [7] R.P Agarwal, M. Benchohra and S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions, Acta. Appl. Math. 109 (3) (2010), 973-1033. doi: 10.1007/s10440-008-9356-6
  • [8] A. Belarbi, M. Benchohra and A. Ouahab, Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces, Appl. Anal. 85 (2006), 1459-1470. doi: 10.1080/00036810601066350
  • [9] M. Belmekki, M. Benchohra and L. Górniewicz, Functional differential equations with fractional order and infinite delay, Fixed Point Theory 9 (2008), 423-439.
  • [10] M. Benchohra, J.R. Graef and S. Hamani, Existence results for boundary value problems with non-linear fractional differential equations, Appl. Anal. 87 (7) (2008), 851-863. doi: 10.1080/00036810802307579
  • [11] M. Benchohra, S. Hamani and S.K. Ntouyas, Boundary value problems for differential equations with fractional order, Surv. Math. Appl. 3 (2008), 1-12.
  • [12] M. Benchohra, J. Henderson and S. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, New York, NY, USA, 2006. doi: 10.1155/9789775945501
  • [13] M. Benchohra, J. Henderson, S.K. Ntouyas and A. Ouahab, Existence results for functional differential equations of fractional order, J. Math. Anal. Appl. 338 (2008), 1340-1350. doi: 10.1016/j.jmaa.2007.06.021
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  • [22] A.A. Kilbas, B. Bonilla and J. Trujillo, Nonlinear differential equations of fractional order in a space of integrable functions, Dokl. Ross. Akad. Nauk 374 (4) (2000), 445-449.
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Bibliografia
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