On the Smoothness of the Solution of Fuzzy Volterra Integral Equations of the Second Kind with Weakly Singular Kernels. (1st July 2021)

• Record Type: Journal Article
• Authors: Alijani, Zahra; Kangro, Urve
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 7(2021)
• Page Start: 819
• Page End: 833
• Publication Date: 2021-07-01
• Subjects: Fuzzy integral equation -- smoothness of the solution -- weakly singular kernel; 65L05 -- 34K06 -- 34K28; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1931312
• Languages: English
• ISSNs: 0163-0563

Abstract

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.