Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

Preprint English OPEN
Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.;

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a represe... View more
  • References (25)
    25 references, page 1 of 3

    [1] M.H. Atabakzadeh, M.H. Akrami, G.H. Erjaee, Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations. Appl. Math. Model., 37 (2013), 8903-8911.

    [2] D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional calculus: Models and numerical methods. 2nd edition, World Scientific, Singapore, 2016.

    [3] N.D. Cong, T.S. Doan, S. Siegmund, H.T. Tuan, On stable manifolds for planar fractional differential equations. Appl. Math. Comput., 226 (2014), 157-168.

    [4] W. Deng, C. Li, J. Lu, Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn., 48 (2007), 409-416.

    [5] W. Deng, C. Li, Q. Guo, Analysis of fractional differential equations with multi-orders. Fractals, 15 (2007), 1-10, 2007.

    [6] K. Diethelm, Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution. Journal Europ´een des Syst`emes Automatis´es, 42 (2008), 665-676.

    [7] K. Diethelm, The Analysis of Fractional Differential Equations. Springer-Verlag, Berlin, 2010.

    [8] K. Diethelm, A fractional calculus based model for the simulation of an outbreak of dengue fever. Nonlinear Dynamics 71 (2013), 613-619.

    [9] K. Diethelm, Properties of the solutions to “fractionalized ODE systems, with applications to processes arising in the life sciences. In D. T. Spasic, N. Grahovac, M. Zigic, M. Rapaic, T. M. Atanackovic (Eds.): Proceedings of the International Conference on Fractional Differentiation and its Applications 2016, Vol. 1. Faculty of Technical Sciences, Novi Sad (2016), 32-44.

    [10] K. Diethelm, N.J. Ford, Multi-order fractional differential equations and their numerical solution. Applied Mathematics and Computation, 154 (2004), 621-640.

  • Related Organizations (2)
  • Metrics
Share - Bookmark