Miskolc Mathematical Notes HU e-ISSN 1787-2413 Vol. 22 (2021), No. 2, pp. 557–569 DOI: 10.18514/MMN.2021.3619 ON NEW CHEBYSHEV INEQUALITIES VIA FRACTIONAL OPERATORS EMRULLAH AYKAN ALAN, BARIS ¸C ¸ EL ˙ IK, ERHAN SET, AND ZOUBIR DAHMANI Received 27 December, 2020 Abstract. The aim of this paper is to establish several fractional integral inequalities related to the weighted and the extended Chebyshev functional. We use generalized fractional integral operators, new conformable fractional integral operators and Saigo fractional integral operators to prove our results. This study states that our findings are more convenient and efficient than other available results. 2010 Mathematics Subject Classification: 26A33; 26D10; 26D15 Keywords: Chebyshev inequality, generalized fractional integral operators, new conformable fractional integral operators, Saigo fractional integral operators 1. I NTRODUCTION AND PRELIMINARIES The integral inequality theory is very important in applied sciences. For more details, we refer the reader to [1, 2] and the references therein. Moreover, the study of the integral inequalities using fractional integration theory is also of great importance, we refer to [8, 9, 14, 15] for some applications. In this paper, we will be concerned with the extended and the weighted Chebyshev functional [2, 9]. So, in this section, we introduce some definitions and some published results that have motivated the present work; we begin by recalling the following definition. Definition 1. If f and g are two integrable functions on [a, b] and p is a positive and integrable function on [a,b], Chebyshev functional is given by the following quantity T( f , g, p) :=  b a p(x)dx  b a f (x)g(x) p(x)dx −  b a f (x) p(x)dx  b a g(x) p(x)dx. Related to the above quantity, in [6], N. Elezovic et al. proved the following integ- ral result: © 2021 Miskolc University Press