The Regularization q-Homotopy Analysis Method for (1 and 2) –Dimensional Non-linear First Kind Fredholm Integral Equations

In this paper, the solutions of(1 and 2)- dimensional non-linear first kind Fredholm integral equations are studied by combine the q-homotopy analysis method (q-HAM) [2- 11] and the regularization method [16,17]. The utilization of this technique depends on converting the first kind Fredholm Integral Equations to the second kind of equations by applying the regularization method. Then q-HAM is employed to the resulting second kind of equations to obtain a solution. Some illustrative examples are given to demonstrate the validity and applicability of this technique.