The main intention of this article is that new techniques of existence theory are used to derive some required criteria pertinent to a given fractional multi-term problem and its inclusion version. In such an approach, we do our research on a fractional integral equation corresponding to the mentioned BVPs. In more precise words, by virtue of this integral equation, we construct new operators which belong to a special category of functions named α-admissible and α-ψ-contraction maps coupled with operators having (AEP)-property. Next, by considering some new properties on the existing Banach space having properties (B) and \((C_{\alpha })\), our argument for ensuring the existence of solutions is completed. In addition, we also add two simulative examples to review our findings by a numerical view.

本文的主要目的是使用存在理论的新技术来得出与给定分数阶多项式问题及其包含形式有关的一些必需准则。通过这种方法，我们对对应于上述BVP的分数积分方程进行了研究。在更精确的话，凭借本积分方程，我们构建属于命名的功能的特殊类新运营商α -admissible和α - ψ -contraction映射与具有（AEP）-property运算符。接下来，通过考虑现有Banach空间上具有属性（B）和\（（C _ {\ alpha}）\）的一些新属性，我们关于确保解决方案存在的论据已经完成。此外，我们还添加了两个模拟示例，以通过数值视图回顾我们的发现。