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Remarks for one-dimensional fractional equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
n this paper we study a class of one-dimensional Dirichlet boundary value problems involving the Caputo fractional derivatives. The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result. Concrete examples of applications are presented.
Rocznik
Strony
691--698
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
  • University of Reggio Calabria and CRIOS University Bocconi of Milan Via dei Bianchi presso Palazzo Zani 89127 Reggio Calabria, Italy
autor
  • Dipartimento P.A.U. Università degli Studi Mediterranea di Reggio Calabria Salita Melissari - Feo di Vito 89124 Reggio Calabria, Italy
Bibliografia
  • [1] R.P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. 109 (2010), 973–1033.
  • [2] G.A. Afrouzi, A. Hadjian, G. Molica Bisci, Some results for one dimensional fractional problems (submitted).
  • [3] B. Ahmad, J.J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58 (2009), 1838–1843.
  • [4] C. Bai, Impulsive periodic boundary value problems for fractional differential equation involving Riemann-Liouville sequential fractional derivative, J. Math. Anal. Appl. 384 (2011), 211–231.
  • [5] C. Bai, Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89 (2011), 1–19.
  • [6] Z. Bai, H. Lu, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005), 495–505.
  • [7] M. Benchohra, S. Hamani, S.K. Ntouyas, Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear Anal. 71 (2009), 2391–2396.
  • [8] M. Galewski, G. Molica Bisci, Existence results for one-dimensional fractional equations (submitted).
  • [9] S. Heidarkhani, Multiple solutions for a nonlinear perturbed fractional boundary value problem, Dynamic Systems and Applications (to appear).
  • [10] S. Heidarkhani, Infinitely many solutions for nonlinear perturbed fractional boundary value problems, preprint.
  • [11] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
  • [12] F. Jiao, Y. Zhou, Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl. 62 (2011), 1181–1199.
  • [13] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
  • [14] A. Kristály, V. Radulescu, Cs. Varga, Variational Principles in Mathematical Physics, Geometry, and Economics: Qualitative Analysis of Nonlinear Equations and Unilateral Problems, Encyclopedia of Mathematics and its Applications, No. 136, Cambridge University Press, Cambridge, 2010.
  • [15] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
  • [16] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [17] B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 401–410.
  • [18] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integral and Derivatives: Theory and Applications, Gordon and Breach, Longhorne, PA, 1993.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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