This article is a study on the (k,s)-Riemann-Liouville fractional integral, a generalization of the Riemann-Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore, we make the estimation of the Box dimension of the graph of continuous functions after the extended integral. It presents that the upper Box dimension of the (k,s)-Riemann-Liouville fractional integral for any continuous functions is no more than the upper Box dimension of the functions on the unit interval I=[0,1], which indicates that the upper Box dimension of the integrand f(x) will not be increased by the σ-order (k,s)-Riemann-Liouville fractional integral ksD−σf(x) where σ>0 on I. Additionally, we prove that the fractal dimension of ksD−σf(x) of one-dimensional continuous functions f(x) is still one.

Chitosan (CTS) is widely used in agriculture as a soil amendment, plant growth regulator and promoter of cold resistance. However, the effects of CTS on strawberry seedlings under the combined stress of high-temperature and high-light are unclear. In this study, Xuelixiang strawberry was used as a test material, and 100 mg·kg-1 CTS solution was sprayed onto the leaves. We measured the chlorophyll content, membrane peroxidation, reactive oxygen species content, antioxidant enzyme content, AsA-GSH cycle activity and other related indicators of strawberry seedling leaves under the combined stress of high-temperature and high-light and found that CTS can increase the contents of antioxidants, increase the contents of osmotic adjustment substances, increase the activity of antioxidant enzymes activity,; remove reactive oxygen species over time, reduce the damage of reactive oxygen species to photosynthetic organs and cell membranes, and improve the photosynthesis efficiency of leaves of strawberry plants under high-temperature and high-light stress, thereby reducing damage to strawberry seedlings caused by high-temperature and high-light.

In large-capacity energy storage systems, instructions are decomposed typically using an equalized power distribution strategy, where clusters/modules operate at the same power and durations. When dispatching shifts from stable single conditions to intricate coupled conditions, this distribution strategy inevitably results in increased inconsistency and hastened system aging. This paper presents a novel differentiated power distribution strategy comprising three control variables: the rotation status, the operating boundaries for both Depth of Discharge (DOD) and C-rates (C) within a control period. The proposed strategy integrates an aging cost prediction model developed to express the mapping relationship between these control variables and aging costs. Additionally, it incorporates the multi-colony particle swarm optimization (Mc-PSO) algorithm into the optimization model to minimize aging costs. The aging cost prediction model consists of three functions: predicting health features (HFs) based on the cumulative charge/discharge throughput quantity and operating boundaries, characterizing HFs as comprehensive scores, and calculating aging costs using both comprehensive scores and residual equipment value. Further, we elaborated on the engineering application process for the proposed control strategy. In the simulation scenarios, this strategy prolonged the service life by 14.62%, reduced the overall aging cost by 6.61%, and improved module consistency by 21.98%, compared with the traditional equalized distribution strategy. In summary, the proposed strategy proves effective in elongating service life, reducing overall aging costs, and increasing the benefit of energy storage systems in particular application scenarios.