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- Title
Dynamic Inequalities of Two-Dimensional Hardy Type via Alpha-Conformable Derivatives on Time Scales.
- Authors
El-Deeb, Ahmed A.; El-Bary, Alaa A.; Awrejcewicz, Jan; Nonlaopon, Kamsing
- 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 = h Z . Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.
- Subjects
JENSEN'S inequality; INTEGRAL inequalities
- Publication
Symmetry (20738994), 2022, Vol 14, Issue 12, p2674
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym14122674