Dynamic Hardy type inequalities via alpha-conformable derivatives on time scales

We prove new Hardy-type $\alpha$-conformable dynamic inequalities on time scales. Our results are proved by using Keller's chain rule, the integration by parts formula, and the dynamic H\"{o}lder inequality on time scales. When $\alpha=1$, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous, discrete, and quantum inequalities.Comment: 27 page

Some New Inverse Hilbert Inequalities on Time Scales

Several inverse integral inequalities were proved in 2004 by Yong. It is our aim in this paper to extend these inequalities to time scales. Furthermore, we also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as special cases. Our results are proved using some algebraic inequalities, inverse Hölder’s inequality and inverse Jensen’s inequality on time scales. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities

Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform

Our work is based on the multiple inequalities illustrated in 2020 by Hamiaz and Abuelela. With the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalize a number of those inequalities to a general time scale. Besides that, in order to get new results as special cases, we will extend our results to continuous and discrete calculus

Dynamic Hardy–Copson-Type Inequalities via (<i>γ</i>,<i>a</i>)-Nabla-Conformable Derivatives on Time Scales

We prove new Hardy–Copson-type (γ,a)-nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller’s chain rule, the integration by parts formula, and the dynamic Hölder inequality on time scales. When γ=1, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous and discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities

A Variety of Nabla Hardy’s Type Inequality on Time Scales

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 (γ,a)-nabla Hölder inequality on time scales. The inequalities proved here extend and generalize existing results in the literature. Further, in the case when γ=1, 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

On Some Important Class of Dynamic Hilbert&rsquo;s-Type Inequalities on Time Scales

In this important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, H&ouml;lder inequality, and Jensen&rsquo;s inequality on time scales