In this paper, we investigate the existence and uniqueness of the S-asymptotically \(\omega \)-periodic mild solutions to a class of multi-term time-fractional measure differential equations with nonlocal conditions in an ordered Banach spaces. Firstly, we look for suitable concept of S-asymptotically \(\omega \)-periodic mild solution to our concern problem, by means of Laplace transform and \((\beta ,\gamma _k)\)-resolvent family \(\{S_{\beta ,\gamma _k}(t)\}_{t\ge 0}\). Secondly, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed fractional measure differential equations, and obtain the existence of maximal and minimal S-asymptotically \(\omega \)-periodic mild solutions for the mentioned system. Finally, as the application of abstract results, an example is given to illustrate our main results.

在本文中，我们研究了有序 Banach 空间中一类具有非局部条件的多项时间分数测度微分方程的S渐近\(\omega \)周期温和解的存在性和唯一性。首先，我们通过拉普拉斯变换和\ ( (\beta ,\gamma _k)\)求解族\(\ {S_{\beta ,\gamma _k}(t)\}_{t\ge 0}\)。其次，在延迟分数阶测度微分方程存在下解和上解的情况下，构造单调迭代法，得到该系统存在最大和最小S-渐近\(\omega\) -周期温和解。最后，作为抽象结果的应用，给出了一个例子来说明我们的主要结果。