Numerical Solution of Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Successive Approximation

This study aims to discuss the existence and uniqueness of solution of fuzzy Volterra integral equations with piecewise continuous kernels. These types of problems are often encountered in balancing issues for systems with hereditary dynamics, such as electric load leveling. The method of successive approximations is applied and the main theorems are proved based on the method. Some examples are discussed and the results are presented for different values of $\mu$ by plotting several graphs. In order to show the accuracy of the method, the results have compared with the homotopy analysis method.