Fuzzy Volterra Integral Equations with Piecewise Continuous Kernels: Theory and Numerical Solution

This research focuses on addressing both linear and nonlinear fuzzy Volterra integral equations that feature piecewise continuous kernels. The problem is tackled using the method of successive approximations. The study discusses the existence and uniqueness of solutions for these fuzzy Volterra integral equations with piecewise kernels. Numerical results are obtained by applying the successive approximations method to examples for both linear and nonlinear scenarios. Error analysis graphs are plotted to illustrate the accuracy of the method. Furthermore, a comparative analysis is presented through graphs of approximate solutions for different fuzzy parameter values. To highlight the effectiveness and significance of the successive approximations method, a comparison is made with the traditional homotopy analysis technique. The results indicate that the successive approximation method outperforms the homotopy analysis method in terms of accuracy and effectiveness.