PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2015 | 13 | 1 |
Tytuł artykułu

An approximation method for fractional integro-differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work, an approximation method is proposed for fractional order linear Fredholm type integrodifferential equations with boundary conditions. The Sinc collocation method is applied to the examples and its efficiency and strength is also discussed by some special examples. The results of the proposed method are compared to the available analytic solutions.
Wydawca

Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-11-09
zaakceptowano
2015-11-25
online
2015-12-16
Twórcy
  • Department of Mathematical
    Engineering, Yildiz Technical University, 34210-Davutpasa-
    Istanbul, Turkey
Bibliografia
  • [1] M.Zarebnia, Z.Nikpour, "Solution of linear Volterra integrodifferentialequations via Sinc functions." International Journalof Applied Mathematics and Computation 2, 1 (2009): 001-010.DOI: 10.0000/ijamc.2010.2.1.63[Crossref]
  • [2] A.Mohsen, M.El-Gamel, "A Sinc-Collocation method for thelinear Fredholm integro-differential equations." Zeitschrift fürangewandte Mathematik und Physik 58, 3 (2007): 380-390.
  • [3] A.Mohsen, M.El-Gamel, "Sinc-collocation Algorithm for SolvingNonlinear Fredholm Integro-differential Equations." BritishJournal of Mathematics & Computer Science 4, 12 (2014): 1693-1700.[Crossref]
  • [4] A.Secer, S.Alkan, M.A.Akinlar, M.Bayram, "Sinc-Galerkinmethod for approximate solutions of fractional order boundaryvalue problems", Boundary Value Problems, vol. 2013, article281, 2013.
  • [5] M.A.Akinlar, A.Secer, M.Bayram, "Numerical solution of fractionalBenney equation", AppliedMathematics and InformationSciences, vol. 8, no. 4, pp. 1633-1637, 2014.[Crossref]
  • [6] M.A.Akinlar, A.Secer, M.Bayram, "Stability, synchronizationcontrol and numerical solution of fractional Shimizu-Moriokadynamical system", Applied Mathematics & Information Sciences,vol. 8, no. 4, pp. 1699-1705, 2014.[Crossref]
  • [7] M.Kurulay, M.A.Akinlar, R.Ibragimov, "computational solutionof a fractional integro-differential equation", Abstract and AppliedAnalysis, 2013/8/12, 2013.
  • [8] F.Stenger, "Approximations via Whittaker’s cardinal function."J. Approx. Theory 17, 222-240 (1976). DOI:10.1016/0021-9045(76)90086-1[Crossref]
  • [9] F.Stengeri, "A sinc-Galerkin method of solution of boundaryvalue problems." Math. Comput. 33, 85-109 (1979).
  • [10] E.T.Whittaker, "On the functions which are represented by theexpansions of the interpolation theory." Proc. R. Soc. Edinb. 35,181-194 (1915).
  • [11] J.M.Whittaker, "Interpolatory Function Theory." CambridgeTracts in Mathematics and Mathematical Physics, vol. 33. CambridgeUniversity Press, London (1935).
  • [12] M.Caputo, M.Fabrizo, "A new Definition of Fractional Derivativewithout Singular Kernel." Progr.Fract.Differ.Appl.1(2015)73–85.
  • [13] A.Atangana, B.Saad, T.Alkahtani, "Analysis of the Keller-SegelModelwith a Fractional Derivativewithout Singular Kernel.", Entropy17(2015) 4439–4453.[Crossref]
  • [14] A.Atangana, J.J.Nieto, "Numerical solution for the model of RLCcircuit via the fractional derivative without singular kernel",Adv.Mech.Eng. 7(10) (2015) 1–7.[WoS]
  • [15] A.Atangana, "On the new fractional derivative and applicationto nonlinear Fisher’s reaction-diffusion equation", AppliedMathematics and Computation, 273 (2016) 948-956[WoS]
  • [16] R.Almeida, D.F.M.Torres, "Necessary and suflcient conditionsfor the fractional calculus of variations with Caputo derivatives."Commun. Nonlinear Sci. Numer. Simul. 16, 1490-1500(2011).[Crossref]
  • [17] J.Rashidinia, M.Nabati, "Sinc-Galerkin and Sinc-Collocationmethods in the solution of nonlinear two-point boundaryvalue problems.", Computational and Applied Mathematics32.2 (2013): 315-330.[WoS][Crossref]
  • [18] A.Mohsen, M.El-Gamel, "A Sinc-Collocation method for thelinear Fredholm integro-differential equations." Zeitschrift fürangewandte Mathematik und Physik 58, 3 (2007): 380-390.
  • [19] M.El-Gamel, A.Zayed, "Sinc-Galerkin method for solving nonlinearboundary-value problems.", Comput. Math. Appl. 48, 1285-1298 (2004).[Crossref]
  • [20] M.Zarebnia, M.Sajjadian, "The sinc-Galerkin method for solvingTroesch’s problem", Mathematical and Computer Modelling 56(2012) 218-228.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_1515_phys-2015-0049
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.