In this paper we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski, trapezoid and Grüss type inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.

Using generalized Caputo fractional left and right vectorial Taylor formulae, we establish mixed Ostrowski Grüss type inequalities involving several Banach algebra valued functions. The estimates are with respect to all norms ∥·∥p, 1 ≤p ≤∞.