Abstract
We established some new α-conformable dynamic inequalities of Hardy–Knopp type. Some new generalizations of dynamic inequalities of α-conformable Hardy type in two variables on time scales are established. Furthermore, we investigated Hardy’s inequality for several functions of α-conformable calculus. Our results are proved by using two-dimensional dynamic Jensen’s inequality and Fubini’s theorem on time scales. When α=1, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we derived Hardy’s inequality for T=R,T=Z and T=hZ. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference25 articles.
1. Note on a theorem of Hilbert;Hardy;Math. Z.,1920
2. Notes on some points in the integral calculus (lx);Hardy;Messenger Math.,1925
3. Elementary theorems concerning power series with positive coeficients and moment constants of positive functions;Littlewood;J. Reine Angew. Math.,1927
4. Hardy, G.H., Littlewood, J.E., and Polya, G. (1952). Inequalities, Cambridge University Press. [2nd ed.].
5. Notes on some points in the integral calculus (lxit);Hardy;Messenger Math.,1928