This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s with Specht’s ratio and mean inequalities. To get the results, we used the Specht’s ratio function and its applications for reverse inequalities of Hilbert-type. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type.

In this article, some fractional Hardy-Leindler-type inequalities will be illustrated by utilizing the chain law, Hölder’s inequality, and integration by parts on fractional time scales. As a result of this, some classical integral inequalities will be obtained. Also, we would have a variety of well-known dynamic inequalities as special cases from our outcomes when α = 1 .

In this article, we establish several new generalized Hardy-type inequalities involving several functions on time-scale nabla calculus. Furthermore, we derive some new multidimensional Hardy-type inequalities on time scales nabla calculus. The main results are proved by applying Minkowski’s inequality, Jensen’s inequality and Arithmetic Mean–Geometric Mean inequality. As a special case of our results, when $\mathbb{T}=\mathbb{R},$ we obtain refinements of some well-known continuous inequalities and when $\mathbb{T}=\mathbb{N}$, the results which are essentially new.

In this paper, we prove some new generalized inequalities of Hilbert-type on time scales nabla calculus by applying Hölder’s inequality, Young’s inequality, and Jensen’s inequality. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.

This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Hölder inequalities on $\mathbb{T}$. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power $\beta ,$$\beta >1.$ The main results are proved by using Specht’s ratio, chain rule and Jensen’s inequality. Our results (when $\mathbb{T}=\mathbb{N}$) are essentially new. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.