In this work, we study the existence of solutions of nonlinear fractional coupled system of $\varphi $-Hilfer type in the frame of Banach spaces. We improve a property of a measure of noncompactness in a suitably selected Banach space. Darbo’s fixed point theorem is applied to obtain a new existence result. Finally, the validity of our result is illustrated through an example.

中文翻译：

---

Banach空间中-Hilfer分数阶微分系统的理论研究

在这项工作中，我们研究了Banach空间框架下$\varphi $ -Hilfer型非线性分数耦合系统解的存在性。我们改进了适当选择的巴纳赫空间中的非紧性度量的性质。应用达博不动点定理得到新的存在结果。最后，通过一个例子说明了我们结果的有效性。