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Convergence of Homotopy Perturbation Method for Solving of Two-Dimensional Fuzzy Volterra Functional Integral Equations

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Advanced Computing in Industrial Mathematics (BGSIAM 2017)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 793))

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Abstract

In this paper, Homotopy Perturbation Method (HPM) is applied to solve two-dimensional fuzzy Volterra functional integral equations (2D-FVFIE). We use parametric form of fuzzy functions and convert a 2D-FVFIE to a system of Volterra functional integral equations with three variables in crisp case. We use the HPM to find the approximate solution of the converted system, which is the approximate solution for 2D-FVFIE. Also, the existence and uniqueness of the solution and convergence of the proposed methods are proved. The main tool in this discussion is fixed point theorem. The error estimate in this method is also given. Finally, we give some examples to demonstrate the accuracy of the method. The solved problems reveal that the proposed method is effective and simple, and in some cases, it gives the exact solution.

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Acknowledgements

Research was partially supported by Fund FP17-FMI-008, Fund Scientific Research, University of Plovdiv Paisii Hilendarski, Bulgaria.

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Authors and Affiliations

  1. FMI, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000, Plovdiv, Bulgaria

    Atanaska Georgieva

  2. FMNS, University of Pristina “Hasan Prishtina”, str “Nena Tereze”, 10000, Prishtine, Kosovo

    Artan Alidema

Authors
  1. Atanaska Georgieva
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  2. Artan Alidema
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Correspondence to Atanaska Georgieva .

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Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir Georgiev

  2. Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Sofia, Bulgaria

    Michail Todorov

  3. Institute of Mathematics and Informatics and Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Georgiev

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Georgieva, A., Alidema, A. (2019). Convergence of Homotopy Perturbation Method for Solving of Two-Dimensional Fuzzy Volterra Functional Integral Equations. In: Georgiev, K., Todorov, M., Georgiev, I. (eds) Advanced Computing in Industrial Mathematics. BGSIAM 2017. Studies in Computational Intelligence, vol 793. Springer, Cham. https://doi.org/10.1007/978-3-319-97277-0_11

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