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Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations

Published: 10 January 2013
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Abstract

In this paper, the cosine basis neural network algorithm is introduced for the initial value problem of fractional differential equations. By training the neural network algorithm, we get the numerical solution of the initial value problem of fractional differential equations successfully.

Published in Applied and Computational Mathematics (Volume 2, Issue 6)
DOI 10.11648/j.acm.20130206.19
Page(s) 159-162
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Fractional Differential Equations, Cosine Basis Neural Network Algorithm, Initial Value Problem

References
[1] R. Metzler, J. Klafter, The random walks guide to anomalous diffusion: afractional dynamics approach, Phys. Rep. 339 (1) (2000) 1-77.
[2] I. Podlubny, et al. Matrix approach to discrete fractional calculus II: Partial fractional differential equations, Journal of Computational Physics. 228(2009) 3137-3153.
[3] H.D. Qu, X. Liu. Existence of nonnegative solutions for fractional m-point boundary value problem at resonance. Boundary Value Problems 2013, 2013:127. doi: 10.1186/1687-2770-2013-127
[4] A. Elsaid. Homotopy analysis method for solving a class of fractional partial differential equations, Commun. Nonlinear Sci. Numer Simulat. 16 (2011)3655-3664.
[5] A.A.Kilbsa, H.M.Srivastava, J.J.Trujillo. Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
Cite This Article
  • APA Style

    Luo Xiaodan, Junmin Zhang. (2013). Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations. Applied and Computational Mathematics, 2(6), 159-162. https://doi.org/10.11648/j.acm.20130206.19

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    ACS Style

    Luo Xiaodan; Junmin Zhang. Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations. Appl. Comput. Math. 2013, 2(6), 159-162. doi: 10.11648/j.acm.20130206.19

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    AMA Style

    Luo Xiaodan, Junmin Zhang. Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations. Appl Comput Math. 2013;2(6):159-162. doi: 10.11648/j.acm.20130206.19

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  • @article{10.11648/j.acm.20130206.19,
      author = {Luo Xiaodan and Junmin Zhang},
      title = {Neural Network Method for Numerical Solution of Initial Value Problems of Fractional Differential Equations},
      journal = {Applied and Computational Mathematics},
      volume = {2},
      number = {6},
      pages = {159-162},
      doi = {10.11648/j.acm.20130206.19},
      url = {https://doi.org/10.11648/j.acm.20130206.19},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130206.19},
      abstract = {In this paper, the cosine basis neural network algorithm is introduced for the initial value problem of fractional differential equations. By training the neural network algorithm, we get the numerical solution of the initial value problem of fractional differential equations successfully.},
     year = {2013}
    }
    

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Author Information
  • Department of Mathmatics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, China

  • Department of Mathmatics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, China

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