In this paper, we mainly investigate some new asymptotic properties on mild solutions to a fractional evolution equation in Banach spaces. Under local, global and mixed Lipschitz type conditions on the second variable for neutral and forced functions respectively, we establish some existence results for pseudo $(\omega ,k)$-Bloch periodic and pseudo S-asymptotically $(\omega ,k)$-Bloch periodic mild solutions to the referenced equation on $\mathbb{R}$ by suitable superposition theorems. The results show that the strict contraction of the neutral function for its second variable takes a dominated part in the existence and uniqueness of such solutions compared with the forced function. As subordinate results, we derive existence results of pseudo (S-asymptotically) $(\omega ,k)$-Bloch periodic mild solutions for the sublinear growth of forced function with its second variable. As special cases, we also deduce some existence results for pseudo ω-antiperiodic and pseudo S-asymptotically ω-antiperiodic mild solutions to the considered equation on $\mathbb{R}$.

在本文中，我们主要研究 Banach 空间中分数阶演化方程的温和解的一些新的渐近性质。在局部、全局和混合 Lipschitz 类型条件下，分别针对中性函数和强制函数的第二个变量，我们建立了伪函数的一些存在性结果$(\omega ,k)$-布洛赫周期和伪S -渐近$(\omega ,k)$- 上参考方程的 Bloch 周期性温和解$\mathbb{R}$通过合适的叠加定理。结果表明，与强制函数相比，中性函数对其第二个变量的严格收缩在此类解的存在性和唯一性中起主导作用。作为从属结果，我们推导出伪（S -渐近）的存在性结果$(\omega ,k)$- 具有第二个变量的强制函数的次线性增长的 Bloch 周期性温和解。作为特例，我们还推导出伪ω -反周期和伪S -渐近ω -反周期温和解对所考虑方程的 一些存在性结果$\mathbb{R}$.