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Homotopy Analysis Method to Solve Volterra-Fredholm Fuzzy Integral Equations

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Advanced Computing in Industrial Mathematics (BGSIAM 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 961))

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Abstract

In this paper, we consider the two-dimensional nonlinear Volterra-Fredholm fuzzy integral equation (2D-NVFFIE). Homotopy analysis method (HAM) is used to determine the approximate solution of the investigated equation. We convert fuzzy Volterra-Fredholm integral equation to a system of Volterra-Fredholm integral equations in a crisp case. Hence, we obtain approximate solutions of this system and consequently obtain an approximation for the fuzzy solution of the fuzzy Volterra-Fredholm integral equation. We prove the convergence of the proposed method and find an error estimate between the exact and the approximate solution. A numerical example is given to demonstrate the validity and applicability of the proposed technique.

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Author information

Authors and Affiliations

  1. FMI, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4003, Plovdiv, Bulgaria

    Atanaska Georgieva

  2. Department of MPC, Technical University-Sofia, Plovdiv Branch, 25 Tzanko Djustabanov Street, 4000, Plovdiv, Bulgaria

    Albena Pavlova

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

    Lozanka Trenkova

Authors
  1. Atanaska Georgieva
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  2. Albena Pavlova
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  3. Lozanka Trenkova
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Corresponding author

Correspondence to Atanaska Georgieva .

Editor information

Editors and Affiliations

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

    Ivan Georgiev

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Science, Sofia, Bulgaria

    Hristo Kostadinov

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Science, Sofia, Bulgaria

    Elena Lilkova

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Georgieva, A., Pavlova, A., Trenkova, L. (2021). Homotopy Analysis Method to Solve Volterra-Fredholm Fuzzy Integral Equations. In: Georgiev, I., Kostadinov, H., Lilkova, E. (eds) Advanced Computing in Industrial Mathematics. BGSIAM 2018. Studies in Computational Intelligence, vol 961. Springer, Cham. https://doi.org/10.1007/978-3-030-71616-5_12

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