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The investigation of inequalities involving the fractional differential and integral operators is considered to be important due to its renowned applications among researchers. This paper consigns to the generalizations of certain fractional integral inequalities. The classical Chebychev type inequalities are generalized by involving k− fractional conformable integrals (kFCI), which is the k− analogue of the fractional conformable integrals. We present the main results consisting of the inequalities using one and two fractional parameters kFCI by taking into account the extended Chebyshev functional in the case of synchronous functions. Some certain interesting consequent results of the main inequalities are also depicted.