Solution for the Fuzzy Volterra-Fredholm Integral Equation with Three Variables
DOI:
https://doi.org/10.31185/bsj.Vol21.Iss38.1419Keywords:
Fuzzy nonlinear Volterra-Fredholm; Integral equations; Three Variables; Banach fixed-point theorem (BFP).Abstract
This paper aims to solve fuzzy nonlinear Volterra-Fredholm integral equations in three variables. The formula under study is an important type of nonlinear Volterra-Fredholm equation. The fuzzy integral equation with nonlinear fuzzy kernels is proven with convergence analysis. Furthermore, the study establishes certain properties of the solution. The results also demonstrate that, for the parametric cases of the fuzzy problem formulation, some necessary and sufficient conditions are met for the Lebenszian model of various functions and their derivatives, as well as the use of Lebenszian's rule for the presented problem formulation. The study also demonstrates the existence and uniqueness of solutions in the space of continuous fuzzy functions with a regular criterion, which generalises the space of fuzzy numbers and is based on the contraction condition
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