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2013 | 11 | 3 | 574-593
Tytuł artykułu

Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
3
Strony
574-593
Opis fizyczny
Daty
wydano
2013-03-01
online
2012-12-22
Twórcy
  • Department of Mathematical Analysis, Faculty of Science, Palacký University, 17. listopadu 12, 771 46, Olomouc, Czech Republic, svatoslav.stanek@upol.cz
Bibliografia
  • [1] Al-Mdallal Q.M., Syam M.I., Anwar M.N., A collocation-shooting method for solving fractional boundary value problems, Commun. Nonlinear Sci. Numer. Simul., 2010, 15(12), 3814–3822 http://dx.doi.org/10.1016/j.cnsns.2010.01.020[Crossref][WoS]
  • [2] Çenesiz Y., Keskin Y., Kurnaz A., The solution of the Bagley-Torvik equation with the generalized Taylor collocation method, J. Franklin Inst., 2010, 347(2), 452–466 http://dx.doi.org/10.1016/j.jfranklin.2009.10.007[Crossref]
  • [3] Coputo M., Linear models of dissipation whose Q is almost frequency independent. II, Fract. Calc. Appl. Anal., 2008, 11(1), 4–14
  • [4] Daftardar-Gejji V., Jafari H., Adomian decomposition: a tool for solving a system of fractional differential equations, J. Math. Anal. Appl., 2005, 301(2), 508–518 http://dx.doi.org/10.1016/j.jmaa.2004.07.039[Crossref]
  • [5] Deimling K., Nonlinear Functional Analysis, Springer, Berlin, 1985 http://dx.doi.org/10.1007/978-3-662-00547-7[Crossref]
  • [6] Diethelm K., The Analysis of Fractional Differential Equations, Lecture Notes in Math., 2004, Springer, Berlin, 2010
  • [7] Diethelm K., Ford N.J., Numerical solution of the Bagley-Torvik equation, BIT, 2002, 42(3), 490–507
  • [8] Edwards J.T., Ford N.J., Simpson A.C., The numerical solution of linear multi-term fractional differential equations: systems of equations, J. Comput. Appl. Math., 2002, 148(2), 401–418 http://dx.doi.org/10.1016/S0377-0427(02)00558-7[Crossref]
  • [9] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., 840, Springer, Berlin-New York, 1989
  • [10] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud., 204, Elsevier, Amsterdam, 2006 http://dx.doi.org/10.1016/S0304-0208(06)80001-0[Crossref]
  • [11] Podlubny I., Fractional Differential Equations, Math. Sci. Engrg., 198, Academic Press, San Diego, 1999
  • [12] Raja M.A.Z., Khan J.A., Qureshi I.M., Solution of fractional order system of Bagley-Torvik equation using evolutionary computational intelligence, Math. Probl. Eng., 2011, #675075 [WoS]
  • [13] Ray S.S., Bera R.K., Analytical solution of the Bagley Torvik equation by Adomian decomposition method, Appl. Math. Comput., 2005, 168(1), 398–410 http://dx.doi.org/10.1016/j.amc.2004.09.006[Crossref]
  • [14] Torvik P.J., Bagley R.L., On the appearance of the fractional derivative in the behavior of real materials, Trans. ASME J. Appl. Mech., 1984, 51(2), 294–298 http://dx.doi.org/10.1115/1.3167615[Crossref]
  • [15] Wang Z.H., Wang X., General solution of the Bagley-Torvik equation with fractional-order derivative, Commun. Nonlinear Sci. Numer. Simul., 2010, 15(5), 1279–1285 http://dx.doi.org/10.1016/j.cnsns.2009.05.069[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0141-4
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