Abstract

In this paper. we consider fuzzy Volterra integral equation of the second kind with weakly singular kernel. We prove existence and uniqueness of the solution. When analyzing the convergence of a numerical method for a given integral equation one needs information about the smoothness of the exact solution. We describe the smoothness of the solution, assuming that the sign of the kernel can change only along the horizontal and vertical lines.

中文翻译：

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关于弱奇异核的第二类模糊Volterra积分方程解的平滑性

摘要

在本文中。我们考虑具有弱奇异核的第二类模糊Volterra积分方程。我们证明解的存在性和唯一性。在分析给定积分方程的数值方法的收敛性时，需要有关精确解的平滑度的信息。我们描述了解决方案的平滑度，假设内核的符号只能沿水平线和垂直线变化。