Fractional Order Differential Inclusions via the Topological Transversality Method

• Mouffak Benchohra ^[1] ; Naima Hamidi ^[1]
  1. [1] Université de Sidi Bel Abbès Laboratoire de Mathématiques
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 13, Nº. 2, 2011, págs. 139-149
• Idioma: inglés
• DOI: 10.4067/S0719-06462011000200008
• Enlaces
  • Texto completo
• Resumen
  • español

    El objetivo de este trabajo es presentar nuevos resultados sobre la existencia de soluciones para una clase de problemas de contorno para inclusiones diferenciales derivados de la participación de Caputo fraccionada. Nuestro enfoque se basa en el método de la transversalidad topológica.

  • English

    The aim of this paper is to present new results on the existence of solutions for a class of boundary value problem for differential inclusions involving the Caputo fractional derivative. Our approach is based on the topological transversality method.

• Referencias bibliográficas
  • Agarwal, R.P,Benchohra, M,Hamani, S. (2010). A survey on existence result for boundary value problems of nonlinear fractional differential...
  • Aubin, J. P,Cellina, A. (1984). Differential Inclusions. Springer-Verlag. Berlin-Heidelberg, New York.
  • Belarbi, A,Benchohra, M,Hamani, S,Ntouyas, S.K. (2007). Perturbed functional differential equations with fractional order. Commun. Appl. Anal....
  • Belarbi, A,Benchohra, M,Ouahab, A. (2006). Uniqueness results for fractional functional differential equations with infinite delay in Fréchet...
  • Benchohra, M,Graef, J. R,Hamani, S. (2008). Existence results for boundary value problems of nonlinear fractional differential equations with...
  • Benchohra, M,Hamani, S. (2008). Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative. Topol. Methods...
  • Benchohra, M,Hamani, S,Ntouyas, S.K. (2008). Boundary value problems for differential equations with fractional order. Surv. Math. Appl. 3....
  • Benchohra, M,Henderson, J,Ntouyas, S.K,Ouahab, A. (2008). Existence results for fractional order functional differential equations with infinite...
  • Boucherif, A,Chiboub-Fellah Merabet, N. (2005). Boundary value problems for first order multivalued differential systems. Arch. Math. (Brno....
  • Chang, Y.-K,Nieto, J.J.. (2009). Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput....
  • Diethelm, K,Freed, A.D. (1999). Scientifice Computing in Chemical Engi-neering II-Computational Fluid Dynamics, Reaction Engineering and Molecular...
  • Diethelm, K,Ford, N. J. (2002). Analysis of fractional differential equations. J. Math. Anal. Appl. 265. 229-248
  • Deimling, K. (1992). Multivalued Differential Equations,Walter De Gruyter.
  • Eloe, P. W,Henderson, J. (1984). Nonlinear boundary value problems and a priori bounds on solutions. SIAM J. Math. Anal. 15. 642-647
  • Frigon, M. (1990). M., Application de la transversalite topologique a des problemes non lineaires pour des equations differentielles ordinaires....
  • Glockle, W. G,Nonnenmacher, T. F. (1995). A fractional calculus approach of self-similar protein dynamics. Biophys. J. 68. 46-53
  • Granas, A. (1976). Sur la méthode de continuité de Poincaré. C. R. Acad. Sci. Paris.
  • Granas, A,Dugundji, J. (2003). Fixed Point Theory. Springer Verlag. New York.
  • Henderson, J,Tisdell, C.C. (2004). Topological transversality and boundary value problems on time scales. J. Math. Anal. Appl. 289. 110-125
  • Hilfer, R. (2000). Applications of Fractional Calculus in Physics. World Scientific. Singapore.
  • Kilbas, A.A,Srivastava, Hari M,Trujillo, Juan J. (2006). Theory and Applications of Fractional Differential Equations. Elsevier Science B.V.,....
  • Lakshmikantham, V,Leela, S,Vasundhara, J. (2009). Theory of Fractional Dynamic Systems. Cambridge Academic Publishers. Cambridge.
  • Lasota, A,Opial, Z. (1965). An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol....
  • Metzler, F,Schick, W,Kilian, H. G,Nonnenmacher, T. F. (1995). Relaxation in filled polymers: A fractional calculus approach. J. Chem. Phys....
  • Miller, K. S,Ross, B. (1993). An Introduction to the Fractional Calculus and Differential Equations. John Wiley. New York.
  • Ouahab, A. (2008). Some results for fractional boundary value problem of differential inclusions. Nonlinear Anal. 69. 3877-3896
  • Oldham, K.B,Spanier, J. (1974). The Fractional Calculus. Academic Press. New York, London.
  • Podlubny, I. (1999). Fractional Differential Equations. Academic Press. San Diego.
  • Samko, S. G,Kilbas, A. A,Marichev, O. I. (1993). Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach. Yverdon.
  • Yu, C,Gao, G. (2005). Existence of fractional differential equations. J. Math. Anal. Appl. 310. 26-29
  • Zhang, S. (2006). Positive solutions for boundary-value problems of nonlinear fractional diffrential equations, Electron. J. Differential...