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Numerical and Analytic Method for Solving Proposal Fuzzy Nonlinear Volterra Integral Equation by Using Homotopy Analysis Method

Received: 4 May 2016     Accepted: 14 May 2016     Published: 28 May 2016
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Abstract

In this paper, we presented the convergence of the solution for the nonlinear fuzzy volterra integral equation with high computational and complexity to find the solution in analytical method, so we describable this solution by using Homotopy analysis method, by using Banach fixed point theory for existence and uniqueness. That with explained numerical examples. Finally using the MAPLE program to solve our problem.

Published in American Journal of Applied Mathematics (Volume 4, Issue 3)
DOI 10.11648/j.ajam.20160403.15
Page(s) 142-157
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), 2016. Published by Science Publishing Group

Keywords

Fuzzy Number, Volterra nonlinear Integral Equation, Operator of Fuzzy Number, Fuzzy Integral, Homotopy Analysis Method

References
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  • APA Style

    Sameer Qasim Hasan, Alan Jalal Abdulqader. (2016). Numerical and Analytic Method for Solving Proposal Fuzzy Nonlinear Volterra Integral Equation by Using Homotopy Analysis Method. American Journal of Applied Mathematics, 4(3), 142-157. https://doi.org/10.11648/j.ajam.20160403.15

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    ACS Style

    Sameer Qasim Hasan; Alan Jalal Abdulqader. Numerical and Analytic Method for Solving Proposal Fuzzy Nonlinear Volterra Integral Equation by Using Homotopy Analysis Method. Am. J. Appl. Math. 2016, 4(3), 142-157. doi: 10.11648/j.ajam.20160403.15

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    AMA Style

    Sameer Qasim Hasan, Alan Jalal Abdulqader. Numerical and Analytic Method for Solving Proposal Fuzzy Nonlinear Volterra Integral Equation by Using Homotopy Analysis Method. Am J Appl Math. 2016;4(3):142-157. doi: 10.11648/j.ajam.20160403.15

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  • @article{10.11648/j.ajam.20160403.15,
      author = {Sameer Qasim Hasan and Alan Jalal Abdulqader},
      title = {Numerical and Analytic Method for Solving Proposal Fuzzy Nonlinear Volterra Integral Equation by Using Homotopy Analysis Method},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {3},
      pages = {142-157},
      doi = {10.11648/j.ajam.20160403.15},
      url = {https://doi.org/10.11648/j.ajam.20160403.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160403.15},
      abstract = {In this paper, we presented the convergence of the solution for the nonlinear fuzzy volterra integral equation with high computational and complexity to find the solution in analytical method, so we describable this solution by using Homotopy analysis method, by using Banach fixed point theory for existence and uniqueness. That with explained numerical examples. Finally using the MAPLE program to solve our problem.},
     year = {2016}
    }
    

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    T1  - Numerical and Analytic Method for Solving Proposal Fuzzy Nonlinear Volterra Integral Equation by Using Homotopy Analysis Method
    AU  - Sameer Qasim Hasan
    AU  - Alan Jalal Abdulqader
    Y1  - 2016/05/28
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    N1  - https://doi.org/10.11648/j.ajam.20160403.15
    DO  - 10.11648/j.ajam.20160403.15
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    EP  - 157
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20160403.15
    AB  - In this paper, we presented the convergence of the solution for the nonlinear fuzzy volterra integral equation with high computational and complexity to find the solution in analytical method, so we describable this solution by using Homotopy analysis method, by using Banach fixed point theory for existence and uniqueness. That with explained numerical examples. Finally using the MAPLE program to solve our problem.
    VL  - 4
    IS  - 3
    ER  - 

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Author Information
  • College of Education, Department of Mathematics, Al-Mustansiriya University, Baghdad, Iraq

  • College of Education, Department of Mathematics, Al-Mustansiriya University, Baghdad, Iraq

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