Microbial survival and growth modeling in frame of nonsingular fractional derivatives

Abstract

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.