This paper discusses a multi-term time-fractional delay differential equation in a real Hilbert space. An iterative scheme for a multi-term time-fractional differential equation is established using Rothe's method. The method of semi-discretization is extended to this kind of time fractional problem with delay in the case that the time delay parameter $\nu >0$ satisfies $\nu\leq T$, where $T$ denotes the final time. We apply the accretivity of the operator $A$ in an iterative scheme to establish the existence and regularity of strong solutions to the considered problem. Finally, an example is provided to demonstrate the abstract result.

翻译：本文在实Hilbert空间中讨论了一类带延迟的多项时间分数阶延迟微分方程。利用Rothe方法建立了多项时间分数阶微分方程的迭代格式，将半离散化方法推广至时间延迟参数$\nu >0$满足$\nu\leq T$（其中$T$表示终端时间）的此类时间分数阶延迟问题。通过迭代格式中算子$A$的散度性，建立了所考虑问题强解的存在性与正则性。最后，通过一个算例验证了该抽象结论。