New View on Nonlinear Picture Fuzzy Integral Equations

In this article, we solve the second type of nonlinear Volterra picture fuzzy integral equation (NVPFIE) using an accelerated form of the Adomian decomposition method (ADM). Based on (alpha,delta, beta)-cut, we convert the NVPFIE to the nonlinear Volterra integral equations in a crisp form. An accelerated version of the ADM is used to solve this transformed system, which is based on a new formula for the Adomian polynomial. The sufficient condition that guarantees a unique solution is obtained using this new Adomian polynomial, error estimates are given, and the convergence of the series solution is proven. Numerical cases are discussed to illustrate the effectiveness of this approach.

Automated summary

In this article, the second type of nonlinear Volterra picture fuzzy integral equation (NVPFIE) is solved using an accelerated form of the Adomian decomposition method (ADM). By converting the NVPFIE to the nonlinear Volterra integral equations based on (alpha,delta, beta)-cut, the transformed system is solved using an accelerated version of the ADM with a new formula for the Adomian polynomial. The sufficient condition for obtaining a unique solution is derived using this new Adomian polynomial, along with error estimates and proof of convergence of the series solution. Numerical cases are presented to demonstrate the effectiveness of this approach.