IntroductionLactic acid bacteria are abundantly found in food and also found in the digestive tract of animals and humans 1) . The term Lactobacillus was increasingly being acknowledged in early 20 th century 2) . All strains of LAB are categorized as probiotics however, the members of two genera Lactobacillus sp. and Bifidobacterium sp. are a having vast number of probiotics 3) . But most of the probiotics belong to the genus Lactobacillus 4) . Activity against undesirable and pathogenic bacteria is the main reason because bacteriocin produced by bacteria has gained an area of interest. Lactic acid bacteria are member of diverse group of industrially important and safe bacteria. These bacteria are not only used as probiotics and starter cultures, but are also involved in industrial biotechnology to biocatalyse and transform the renewable feedstocks to economically im-

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The main purpose of this research is to use a fractional-mathematical model including Atangana–Baleanu derivatives to explore the clinical associations and dynamical behavior of the tuberculosis. Herein, we used a lately introduced fractional operator having Mittag-Leffler kernel. The existence and inimitability problems to the relevant model were examined through the fixed-point theory. To verify the significance of the arbitrary fractional-order derivative, numerical outcomes were explored from the biological and mathematical viewpoints using the values of model parameters. The graphical simulations show the comparison of the predictor–corrector method (PCM) and Caputo method (CM) for different fractional orders and the results indicated the significant preference of PCM over CM.

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