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