In this article, some integral equations that have been appeared in the study of physical phenomena are investigated by using the unique properties of the extended homotopy analysis method. In other words, the traditional homotopy analy- sis method is extended to a multi-parametric approach. Also, convergence-controller parameters are introduced to approximate the solutions of such linear and nonlinear integral equations. In this framework, the convergence of the proposed strategies is investigated. Several numerical examples are presented to illustrate the accuracy and effectiveness of the proposed approaches. The obtained results and comparison with other methods provide confirmation for the validity of our numerical schemes.
