Some new fractional quantum integral inequalities

In this work, we employ a fractional q -integral on the specific time scale T t 0 = { t : t = t 0 q n , n a nonnegative integer } ∪ { 0 } , where t 0 ∈ R and 0 < q < 1 , to establish two fractional q -integral Chebyshev type inequalities using one or two fractional parameters. Furthermore, other fractional q -integral inequalities related to Cauchy’s inequality, Hölder’s inequality and Minkowski’s inequality are also obtained.