Enhanced Solution of Fuzzy Volterra Integral Equations Using San Transform: Accuracy,Stability,and Efficiency Perspectives

Abstract

This paper presents a transform-based analytical framework for the San Transform-based solution of second-kind fuzzy Volterra integral equations. Essential operational aspects including linearity, shifting, scaling, convolution, and derivative relations are directly obtained and detailed inside the fuzzy transform framework in order to facilitate the efficient application of the proposed San Transform to fuzzy-valued integral equations. The proposed solution process demonstrates faster convergence, lower approximation error, and reduced computational cost when compared with conventional transform-based techniques. A parametric α-level representation is used to handle the fuzzy-valued functions, and the suggested transform framework analyzes the lower and upper limit functions independently. The proposed method's performance is compared to the conventional Laplace Transform using quantitative measures such as computing cost, execution time, and absolute error norms, revealing lower computational costs and higher numerical accuracy. The analysis is conducted under the normal assumptions that the kernel and forcing functions are continuous, limited, and fulfill exponential order criteria to assure the suggested transform's existence and stability.