Some new fractional quantum integral inequalities

Abstract

In this work, we employ a fractional q-integral on the specific time scale Tt0={t:t=t0qn, n a nonnegative integer }∪{0}, where t0∈R and 0<q<1, to establish two fractionalq-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.