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2015 | 13 | 1 |

Tytuł artykułu

On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy of method used in this paper.

Wydawca

Czasopismo

Rocznik

Tom

13

Numer

1

Opis fizyczny

Daty

otrzymano
2015-06-19
zaakceptowano
2015-08-03
online
2015-09-25

Twórcy

  • Faculty of Engineering, Department of Computer Engineering, Tunceli University, Tunceli, Turkey
autor
  • Faculty of Science, Department of Mathematics, Firat University , Elazig, Turkey

Bibliografia

  • [1] J. Cao and C. Xu, A high order schema for the numerical solution of the fractional ordinary differential equations, Journal of Computational Physics, 238(2013), 154-168, 2013.
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  • [8] A. Atangana, Convergence and Stability Analysis of A Novel Iteration Method for Fractional Biological Population Equation, Neural Computing and Applications, 25(5), 1021-1030, 2014.
  • [9] R.S. Dubey, B. Saad, T. Alkahtani and A. Atangana, Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method, Mathematical Problems in Engineering, 2014, Article ID 780929, 7 pages, 2014.
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  • [12] A. Atangana, Numerical solution of space-time fractional derivative of groundwater flow equation, Proceedings of the International Conference of Algebra and Applied Analysis, 6(2), 20 pages, 2012.
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  • [14] Q.K. Katatbeh and F.B.M. Belgacem, Applications of the Sumudu Transform to Fractional Diffirential Equations, Nonlinear Studies, 18(1), 99-112, 2011.
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  • [26] A. Atangana, Exact solution of the time-fractional underground water flowing within a leaky aquifer equation Vibration and Control, 1-8, 2014.
  • [27] K.A. Gepreel, The homotopy perturbation method applied to the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations, Applied Mathematics Letters, 24(8), 1428-1434, 2011.[WoS][Crossref]
  • [28] A. Atangana and D. Baleanu, Nonlinear fractional Jaulent-Miodek and Whitham-Broer-Kaup equations within Sumudu transform, Abstract and Applied Analysis, 9 pages, 2013.
  • [29] A. Atangana and N. Bildik, The Use of Fractional Order Derivative to Predict the Groundwater Flow, Mathematical Problems in Engineering, 2013, Article ID 543026, 9 pages, 2013.
  • [30] Z. Hammouch and T. Mekkaoui, Travelling-wave solutions for some fractional partial differential equation by means of generalized trigonometry functions, International Journal of Applied Mathematical Research, 1, 206-212, 2012.
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Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_1515_math-2015-0052
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