Novel Fractional Dynamic Hardy-Hilbert-Type Inequalities on Time Scales with Applications

The main objective of the present article is to prove some new backward difference dynamic inequalities of Hardy-Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel-Legendre transform, submultiplicative functions. We prove the (gamma,a)-nabla conformable Holder's and Jensen's inequality on time scales. We prove several inequalities due to Hardy-Hilbert inequalities on time scales. Furthermore, we introduce the continuous inequalities and discrete inequalities as special case.

Automated summary

This article proves new backward difference dynamic inequalities of Hardy-Hilbert type on time scales, using the Fenchel-Legendre transform and submultiplicative functions. The (gamma,a)-nabla conformable Holder's and Jensen's inequalities on time scales are also proved, along with several inequalities due to Hardy-Hilbert inequalities on time scales. Additionally, continuous inequalities and discrete inequalities are introduced as special cases.