Innovations of some dynamic estimates combined on time scales

We establish fractional versions of generalizations of the Schweitzer, Kantorovich, Polya–Szego, Cassels, Greub–Rheinboldt, and reverse Minkowski inequalities on time scales. We present that fractional P´olya–Szego’s dynamic inequality generalizes Cassels’ inequality. Time scales calculus unifies and extends discrete, continuous, quantum versions of results.