Existence and Uniqueness of the Solution of Two-dimensional Fuzzy Volterra Integral Equation with Piecewise Kernel

TL;DR

This paper proves the existence and uniqueness of solutions for two-dimensional fuzzy Volterra integral equations with discontinuous kernels, using the collocation method, advancing numerical analysis in complex mathematical models.

Contribution

It provides new theoretical results on solution properties of 2D fuzzy Volterra integral equations with discontinuous kernels, employing the collocation method.

Findings

Established conditions for existence and uniqueness

Applied collocation method for solution analysis

Enhanced understanding of integral equations with discontinuous kernels

Abstract

This study investigates the existence and uniqueness of solutions to Volterra integral equations with discontinuous kernels in both linear and nonlinear cases. The problem is two-dimensional, and the collocation method is employed to analyze the equations. The research aims to provide a comprehensive understanding of the solution properties of these integral equations, which are crucial in various mathematical and physical applications. By examining the existence and uniqueness of solutions, this study contributes to the development of numerical methods for solving Volterra integral equations with discontinuous kernels. The findings of this research have the potential to impact various fields, including physics, engineering, and economics, where integral equations play a significant role in modeling complex phenomena.