On New Unified Bounds for a Family of Functions via Fractional q-Calculus Theory

摘要

The present article deals with the new estimates in q-calculus and fractional q-calculus on a time scale Tt0=0∪t:t=t0qn,n?is?a?nonnegative?integer, where t0∈? and 0q1. The role of fractional time scale q-calculus can be found as one of the prominent techniques to generate some variants for a class of positive functions n?n∈?.Finally, our work will provide foundation and motivation for further investigation on time-fractional q-calculus systems that have an intriguing application in quantum theory and special relativity theory.