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.

边值问题（BVP）从实践和理论的角度都吸引了许多科学家的注意力，因为这些问题在纯科学和应用科学的不同分支中都有显着的应用。由于这一重要特性，本研究旨在开发一种用于求解一类非线性分数BVP的有效数值方法。所提出的方法没有扰动，离散化，线性化或限制性假设，并且以一致收敛序列的形式提供了精确的解决方案。此外，确切的解决方案仅通过求解分数阶线性BVP序列来确定。因此，从实践的角度来看，所提出的技术是有效的并且易于实施。为了获得足够准确的近似解决方案，我们提供了一种迭代算法，该算法在计算上也很有效。最后，给出了四个说明性示例，以验证新技术与其他现有结果相比的优越性。