In this article, the two‐parameter Weibull model (3) is considered for microbial survival curves by new fractional differential operators to analyze some microbial, common reasons of illnesses, and outbreaks, such as Salmonella spp. cocktail in ground turkey thigh, pork shoulder, and turkey breast at isothermal cooking conditions in 50°C, 54°C, 58°C, 62°C, and 66°C, then Listeria monocytogenes and Escherichia coli O157:H7 are considered in ground beef in the same thermal conditions. Results obtained with nonsingular fractional derivatives, including exponential decay and Mittag‐Leffler kernel, are analyzed comparatively with Caputo fractional and integer‐order derivatives for survival ratio of microbial cells. In the sequel, E. coli O157:H7 in ground beef, Salmonella typhimurium and S. enteritidis in boneless pork chops, and background flora in ground pork and at room temperature, 10°C, 7.2°C, and 4.4°C are considered for microbial growth curves by nonsingular fractional operators, and results obtained are compared with Caputo fractional and integer‐order derivatives. All results for advantage and disadvantage of Atangana‐Baleanu and Caputo‐Fabrizio fractional derivatives are discussed in detail.

中文翻译：

---

非奇异分数导数框架下的微生物存活和生长模型

在本文中，新的分数微分算子考虑了两参数的Weibull模型（3）的微生物存活曲线，以分析某些微生物，疾病的常见原因和爆发，例如沙门氏菌。在50°C，54°C，58°C，62°C和66°C等温烹饪条件下，在火鸡大腿，猪肩和火鸡胸肉中调制鸡尾酒，然后将李斯特菌和大肠杆菌O157：H7视为在相同的热条件下将牛肉碎。用Caputo分数阶和整数阶导数比较了使用非奇异分数阶导数（包括指数衰减和Mittag-Leffler核）获得的结果，以了解微生物细胞的存活率。在续集中，大肠杆菌微生物生长曲线的O157：H7，无骨猪排的鼠伤寒沙门氏菌和肠炎沙门氏菌以及猪肉的本底菌群在室温，10°C，7.2°C和4.4°C下被认为是微生物生长曲线的非奇异分数运算符，并将获得的结果与Caputo分数阶和整数阶导数进行比较。详细讨论了Atangana-Baleanu和Caputo-Fabrizio分式衍生物的优缺点的所有结果。