Asymptotic stability in delay nonlinear fractional differential equations

• Ardjouni, Abdelouaheb ^[2] ; Boulares, Hamid ^[1] ; Djoudi, Ahcene ^[1]
  1. [1] Badji Mokhtar University

     Badji Mokhtar University

     Argelia

     
  2. [2] University Souk Ahras.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 35, Nº. 3, 2016, págs. 263-275
• Idioma: inglés
• DOI: 10.4067/S0716-09172016000300004
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of delay nonlinear fractional differential equations of order . By using the Banach’s contraction mapping principle in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided that g (t, 0) = f (t, 0, 0) = 0, which include and improve some related results in the literature.

• Referencias bibliográficas
  • Citas [1] S. Abbas, Existence of solutions to fractional order ordinary and delay differential equations and applications, Electronic Journal...
  • [2] R. P. Agarwal, Y. Zhou, Y. He, Existence of fractional functional differential equations, Computers and Mathematics with Applications...
  • [3] T. A. Burton, B. Zhang, Fractional equations and generalizations of Schaefer’s and Krasnoselskii’s fixed point theorems, Nonlinear Anal....
  • [4] F. Chen, J. J. Nieto, Y. Zhou, Global attractivity for nonlinear fractional differential equations, Nonlinear Analysis: Real Word Applications...
  • [5] F. Ge, C. Kou, Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear fractional differential equations, Applied Mathematics...
  • [6] F. Ge, C. Kou, Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < α < 2, Journal of Shanghai...
  • [7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, (2006).
  • [8] C. Kou, H. Zhou, Y. Yan, Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis,...
  • [9] Y. Li, Y. Chen, I. Podlunby, Mittag—Leffler stability of fractional order nonlinear dynamic systems, Automatica 45, pp. 1965—1969, (2009).
  • [10] Y. Li, Y. Chen, I. Podlunby, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag—Leffler...
  • [11] C. Li, F. Zhang, A survey on the stability of fractional differential equations, Eur. Phys. J. Special Topics. 193, pp. 27—47, (2011).
  • [12] I. Ndoye, M. Zasadzinski, M. Darouach, N. E. Radhy, Observerbased control for fractional-order continuous-time systems, Proceedings of...
  • [13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, (1999).
  • [14] D. R. Smart, Fixed point theorems, Cambridge Uni. Press., Cambridge, (1980).
  • [15] J. Wang, Y. Zhou, M. Feckan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl....