This article focuses on the existence of extremal mild solutions for a class of Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach spaces E. By using a monotone iterative method in the presence of lower and upper solutions, we obtain some existence results of extremal mild solutions for Hilfer fractional evolution equations involving noncompact semigroups. Finally, an example is given to illustrate the effectiveness of the abstract results.

中文翻译：

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非局部条件下希尔弗分数阶演化方程的单调迭代技术

本文关注于有序Banach空间E中具有非局部条件的一类Hilfer分数阶演化方程的极值温和解的存在。通过在上下解的存在下使用单调迭代法，我们得到了涉及非紧半群的希尔弗分数演化方程的极端温和解的存在性结果。最后，通过一个例子说明了抽象结果的有效性。