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Bennett-Leindler Nabla Type Inequalities Via Conformable Fractional Derivatives on Time Scales
(Amer inst Mathematical Sciences-aims, 2022) Makharesh, Samer D.; Askar, Sameh S.; Baleanu, Dumitru; El-Deeb, Ahmed A.
In this work, we prove several new (gamma, a)-nabla Bennett and Leindler dynamic inequalities on time scales. The results proved here generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using integration by parts, chain rule and Holder inequality for the (gamma, a)-nabla-fractional derivative on time scales.
On Some Dynamic Inequalities of Hilbert's-type on Time Scales
(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitrru; Shah, Nehad Ali; Abdeldaim, Ahmed; El-Deeb, Ahmed A.
In this article, we will prove some new conformable fractional Hilbert-type dynamic inequalities on time scales. These inequalities generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, conformable fractional Ho center dot lder inequalities, and conformable fractional Jensen's inequalities on time scales.

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