American Journal of Applied Mathematics

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

Received: 04 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.

DOI 10.11648/j.ajam.20160403.15
Published in American Journal of Applied Mathematics (Volume 4, Issue 3, June 2016)
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), 2024. 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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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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  • 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://download.sciencepg.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
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    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.
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