A New Iterative Method for the Numerical Solution of High-Order Non-linear Fractional Boundary Value Problems

The boundary value problems (BVPs) have attracted the attention of many scientists from both practical and theoretical points of view, for these problems have remarkable applications in different branches of pure and applied sciences. Due to this important property, this research aims to develop an efficient numerical method for solving a class of non-linear fractional BVPs. The proposed method is free from perturbation, discretization, linearization, or restrictive assumptions, and provides the exact solution in the form of a uniformly convergent series. Moreover, the exact solution is determined by solving only a sequence of linear BVPs of fractional-order. Hence, from practical viewpoint, the suggested technique is efficient and easy to implement. To achieve an approximate solution with enough accuracy, we provide an iterative algorithm that is also computationally efficient. Finally, four illustrative examples are given verifying the superiority of the new technique compared to the other existing results.