Some Inequalities Involving Fractional q-Derivatives Related to the q-Leibniz Rule

In this paper, we present some inequalities for Riemann–Liouville and Caputo q-fractional derivatives related to the q-Leibniz rule. We used one of the inequalities to prove the maximum principle for a time fractional q-Cauchy differential equation. © 2018, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.