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Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay

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Języki publikacji
EN
Abstrakty
EN
In the present paper we investigate the existence of solutions for a system of integral inclusions of fractional order with multiple delay. Our results are obtained upon suitable fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler for the nonconvex case.
Rocznik
Strony
209--222
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Université de Saida Laboratoire de Mathématiques B.P. 138, 20000, Saida, Algeria
autor
  • Université de Sidi Bel-Abbes Laboratoire de Mathématiques B.P. 89, 22000, Sidi Bel-Abbes, Algeria
Bibliografia
  • [1] S. Abbas, M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay, Nonlinear Anal. Hybrid Syst. 3 (2009), 597-604.
  • [2] S. Abbas, M. Benchohra, Impulsive partial hyperbolic differential inclusions of fractional order, Demonstratio Math. XLIII (2010) 4, 775-797.
  • [3] S. Abbas, M. Benchohra, Upper and lower solutions method for the darboux problem for fractional order partial differential inclusions, Int. J. Mod. Math. 5 (2010), 327-338.
  • [4] S. Abbas, M. Benchohra, Fractional order Riemann-Liouville integral equations with multiple time delay, Appl. Math. E-Notes 12 (2012), 79-87.
  • [5] S. Abbas, M. Benchohra, L. Górniewicz, Fractional order impulsive partial hyperbolic differential inclusions with variable times, Discussions Math. Differ. Inclu. Contr. Op-timiz. 31 (2011), 91-114.
  • [6] S. Abbas, M. Benchohra, G.M. N'Guérékata, Topics in Fractional Differential Equa¬tions, Dev. Math. 27, Springer, New York, 2012.
  • [7] S. Abbas, M. Benchohra, Y. Zhou, Fractional order partial functional differential inclusions with infinite delay, Proc. A. Razmadze Math. Inst. 154 (2010), 1-19.
  • [8] J.P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin-Heidelberg, New York, 1984.
  • [9] M. Benchohra, J.R. Graef, S. Hamani, Existence results for boundary value problems of nonlinear fractional differential equations with integral conditions, Appl. Anal. 87 (2008), 851-863.
  • [10] M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equa¬tions with fractional order, Surv. Math. Appl. 3 (2008), 1-12.
  • [11] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for functional differential equations of fractional order, J. Math. Anal. Appl. 338 (2008), 1340-1350.
  • [12] H.F. Bohnenblust, S. Karlin, On a theorem of ville. Contribution to the theory of games, 155—160, Annals of Mathematics Studies, no. 24. Priceton University Press, Princeton, N.G., 1950.
  • [13] C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
  • [14] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
  • [15] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, 1991.
  • [16] H. Covitz, S.B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11.
  • [17] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999.
  • [18] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [19] Sh. Hu, N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, Boston, London, 1997.
  • [20] R.W. Ibrahim, H.A. Jalab, Existence of the solution of fractional integral inclusion with time delay, Misk. Math. Notes 11 (2010) 2, 139-150.
  • [21] A. A. Kilbas, Hari M. Srivastava, Juan J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
  • [22] A.A. Kilbas, S.A. Marzan, Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, Differ. Equ. 41 (2005), 84-89.
  • [23] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991.
  • [24] A. Lasota, 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.
  • [25] K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, London, 1974.
  • [26] B.G. Pachpatte, On Volterra-Fredholm integral equation in two variables, Demonstratio Math. XL (2007) 4, 839-852.
  • [27] B.G. Pachpatte, On Fredholm type integrodifferential equation, Tamkang J. Math. 39 (2008), 85-94.
  • [28] B.G. Pachpatte, On Fredholm type integral equation in two variables, Differ. Equ. Appl. 1 (2009), 27-39.
  • [29] B.G. Pachpatte, Qualitative properties of solutions of certain Volterra type difference equations, Tamsui Oxf. J. Math. Sci. 26 (2010), 273-285.
  • [30] A.N. Vityuk, Existence of solutions of partial differential inclusions of fractional order, Izv. Vyssh. Uchebn., Ser. Mat. 8 (1997), 13-19.
  • [31] A.N. Vityuk, A.V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order, Nonlinear Oscil. 7 (2004), 318-325
Typ dokumentu
Bibliografia
Identyfikator YADDA
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