A Variety of Nabla Hardy’s Type Inequality on Time Scales - Ahmed A. El-Deeb; Samer D. Makharesh; Sameh S. Askar; Jan Awrejcewicz (Mathematics, 2022)
The primary goal of this research is to prove some new Hardy-type ∇-conformable dynamic inequalities by employing product rule, integration by parts, chain rule and <semantics>(γ,a)</semantics>-nabla Hölder inequality on time scales. The inequalities proved here extend and generalize existing results in the literature. Further, in the case when <semantics>γ=1</semantics>, we obtain some well-known time scale inequalities due to Hardy inequalities. Many special cases of the proposed results are obtained and analyzed such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities and new classical conformable fractional integral inequalities.