Abstract
Chebyshev’s inequality is a well-known inequality in the field of inequality theory and yields remarkable results for functions that exhibit synchronous behavior. The study, designed to obtain Chebyshev type inequalities with the help of the Atangana–Baleanu fractional integral operator, which has become the most popular concept of fractional analysis in recent years, aims to obtain general forms for synchronous functions. In the process of obtaining results for synchronized functions within the scope of the study, functional tools such as Atangana–Baleanu fractional integral operator, various mathematical analysis operations and induction were used. The most striking aspect of the findings is that for some special values of the parameter of the fractional integral operator, some of the results can be reduced to the Chebyshev inequality. Compared to the studies in the literature, this study has a unique aspect in that the findings obtained with the help of the Atangana–Baleanu fractional integral operator contain general forms, as well as bringing together a popular concept of synchronous functions and fractional analysis.
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