رجـــــاء كــريم جبــر الابراهيــمي

Several scientific and engineering applications are usually described as integral equations. We propose a numerical approach for solving the type of Fredholm nonlinear boundary value problems in a finite domain. The paper aims to use the q-homotopy analysis method to estimate the solution to test the efficiency of the proposed method. Comparison with updated work is exacted. The obtained results show that the proposed method is very effective and convenient for nonlinear Fredholm integral equations. The interval of convergence of homotopy analysis method, if exists, is increased when using q-homotopy analysis method is more to converge. The result reveals that the q- homotopy analysis method is considered a good method for solving NFIES.