\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points

Abstract Related Papers Cited by
  • In the paper we consider a Dirichlet problem for a fractional differential equation. The main goal is to prove an existence and continuous dependence of solution on functional parameter $u$ for the above problem. To prove it we use a variational method.
    Mathematics Subject Classification: Primary: 34B08, 34A08; Secondary: 49J53.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, 1990.

    [2]

    D. Bors, A. Skowron and S. Walczak, Optimal control and stability of elliptic systems with integral cost functional, Systems Science, 33 (2007), 13-26.

    [3]

    D. Bors and S. Walczak, Nonlinear elliptic systems with variable boundary data, Nonlinear Analysis: Theory, Methods and Applications, 52 (2003), 1347-1364.doi: 10.1016/S0362-546X(02)00179-7.

    [4]

    L. Bourdin, Existence of a weak solution for fractional Euler-Lagrange equations, Journal of Mathematical Analysis and Applications, 399 (2013), 239-251.doi: 10.1016/j.jmaa.2012.10.008.

    [5]

    L. Debnath, Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, 54 (2003), 3413-3442.doi: 10.1155/S0161171203301486.

    [6]

    D. Idczak, Fractional du Bois-Reymond Lemma of Order $\alpha\in(1/2,1)$, Proceedings of the 7th International Workshop on Multidimensional (nD) Systems (nDs), 2011, Poitiers, France.

    [7]

    R. Kamocki and M. Majewski, On a fractional Dirichlet problem, Proceedings of 17th International Conference Methods and Models in Automation and Robotics (MMAR), (2012), 60-63.doi: 10.1109/MMAR.2012.6347911.

    [8]

    A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.

    [9]

    L. Nirenberg, Topics in Nonlinear Functional Analysis, New York University - Courant Institute of Mathematical Sciences - AMS, New York, 1974.

    [10]

    I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198, Academic Press, California, 1999.

    [11]

    S. Walczak, On the continuous dependance on parameters of solutions of the Dirichlet problem: Part I. Coercive case; Part II. The case of saddle points, Bulletin de la Classe des Sciences de l'Académie Royale de Beligique, 6 (1995), 247-261.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(87) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return