## 1 Introduction  
_Prunus_ fruits are constantly studied for their beneficial properties as well as their highly preferred taste. Fruits in general are not consumed in quantities that are suggested by the World Health Organization (WHO) [1]. Efforts have been made to promote their consumption. The genus _Prunus_ is probably spread and known worldwide, which explains the interest in creating new varieties as well as intraspecific hybrids [2]. _Prunus persica_ L. fruits provide a wide range of local and introduced varieties that ripen from June to October. Local varieties are often understudied in terms of their bioactivity. The \"Filina\" peach variety is a native Bulgarian variety that has not been promoted enough, although it has shown its potential. The variety is a result of the combination of \"July Lady\" and \"Maycrest\". Authors have documented its chemical composition as well as its antioxidant properties [3] and enzyme inhibition abilities [4]. The majority of the significant polyphenol compounds, i.e., flavonoids, and phenolic acids can be found in peach fruits [5].  
Phenolic compounds are often associated with enhanced health--both free and bound phenolics, as the main research has focused on free phenolics [6]. The biological advantages of fruit phenolic compounds are widely studied and the results continue to prove the fruits' abilities to positively alter conditions like increased insulin levels, cholesterol levels, cancer cell growth, and inflammation, among others [7]. Phenolic compounds are beneficial not only to the food industry but also to fields like cosmetology and pharmacology. Each research design followed a different extraction approach, as there is no unified extraction method that has shown maximum efficiency. Polarity variation of the solvent has shown that differences exist in the properties of the resulting extracts [8; 9]. The extraction of phenolic compounds is dependent on the duration, temperature, solvent/sample ratio, and specificity of the plant matrix, among others. Ultrasound-assisted extraction is often documented as highly potent for plant-based matrices [10]. It is marked by many advantages, i.e., less time and energy involved, lower temperature, and better extract quality [10].  
Planning, examining, and foreseeing extraction conditions have all been performed with the use of response surface methodology (RSM). RSM is a reliable and promising tool in terms of bioactive compound extraction [11]. It can help create the most favorable, cost-effective, and sustainable conditions (short extraction, low solvent consumption, minimum environmental impact) [12; 13].  
This study attempted to optimize the extraction duration, temperature, and solvent ratio to positively alter the number of phenolic compounds and their respective biological activities. This study contributes to the optimization of antioxidant-rich extracts from fruits using mathematical approaches and is a pilot on the \"Filina\" peaches. The Box-Behnken design was applied to predict the model and to optimize the extraction conditions (temperature, time, liquid/solvent ratio) based on total phenolic and flavonoid contents, as well as antioxidant and enzymatic activities. This work can act as a core for other researchers to assess and quantify the biological activity of _Prunus persica_ L.