In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, Riemann–Liouville nonlinear fractional boundary value problem. Under new minimal conditions on the parameters 0 ≤ s, τ ≤ 1, it is shown that, based on the upper and lower solutions method using Schauder fixed point theorem, the positive solutions in a Sobolev spaces exist. Moreover, our results are illustrated by a numerical example.

中文翻译：

---

分数阶 Sobolev 空间中积分非线性边值问题的正解

在本论文中，我们从科学和工程应用的角度考虑一个重要问题，即 Riemann-Liouville 非线性分数边值问题。在参数0 ≤  s ,  τ  ≤ 1 的新极小条件下，基于Schauder不动点定理的上下解法证明了索伯列夫空间中存在正解。此外，我们的结果用一个数值例子来说明。