(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
In this research article, we present several generalizations of Qi’s inequality on time scales. We establish dynamic versions of Callebaut’s inequality and Cauchy-Schwarz’s inequality on time scales. To establish our results, we apply the diamond-alpha integral and the time scale ∆ or ∇-Riemann-Liouville type fractional integrals. Our findings unify and extend discrete, continuous and quantum analogues.