New View on Nonlinear Picture Fuzzy Integral Equations

Abstract

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 (α,δ,β)-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.

Keywords

• picture fuzzy integral equations of the nonlinear volterra type
• convergence analysis
• Adomian series
• error estimate