This article examines a new approach to solving ordinary differential equations based on Fractional-Calculus theory. Poisson and Sturm-Liouville-type problems are studied, together with different boundary conditions. Each case is analyzed and compared concerning the Finite-Difference method outcome.

翻译：本文研究了一种基于分数阶微积分理论的常微分方程求解新方法。文中探讨了泊松型和斯图姆-刘维尔型问题，并考虑了不同的边界条件。每种情形均被分析并与有限差分法的结果进行了比较。