According to a huge interest in implementation of the fuzzy Volterra integral equations, especially the second kind, researchers have been investigating to solve such equations using numerical methods since analytical ones might not be accessible usually. In this research paper, we introduce a newapproach based on Fibonacci polynomials collocation method to numerically solve them. Several properties of such polynomials were considered to implement in the collocation method due to approximate the solution of the second kind of fuzzy Volterra integral equations. We approved the existence, uniqueness of the solution, convergence and the error analysis of the proposed method in detail. In order to show the authenticity and applicability of the proposed method, we employed several illustrative examples. The numerical results show that the convergence and precision of the recent method were in a good settlement with the exact solution. Also, the calculations of the suggested method are simple and low computational complexity in respect to other methods as an advantage feature of the presented approach.

中文翻译：

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使用斐波那契多项式求解模糊Volterra积分方程的有效方法

由于对实现模糊Volterra积分方程，特别是第二种方程的巨大兴趣，研究人员一直在研究使用数值方法来求解此类方程，因为通常无法使用解析方法。在本文中，我们介绍了一种基于斐波那契多项式搭配方法的新方法，以数值方法对其进行求解。由于近似第二类模糊Volterra积分方程的解，因此考虑在搭配方法中实现此类多项式的若干性质。我们详细认可了该方法的存在性，唯一性，收敛性和误差分析。为了显示所提出方法的真实性和适用性，我们采用了几个说明性的例子。数值结果表明，该方法的收敛性和精度都得到了很好的解决。另外，作为所提出方法的优点，相对于其他方法，所建议方法的计算简单且计算复杂度低。