Abstract
This paper provides novel generalizations by considering the generalized conformable fractional integrals for reverse Copson’s type inequalities on time scales. The main results will be proved using a general algebraic inequality, chain rule, Hölder’s inequality, and integration by parts on fractional time scales. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues. In addition, when α = 1, we obtain some well-known time scale inequalities due to Hardy, Copson, Bennett, and Leindler inequalities.
Highlights
The Hardy discrete inequality is known as: Received: 2 March 2021 ∞ ∑Accepted: 23 March 2021Published: 25 March 2021Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affill =1 l l ∑ w( j) !h ≤ j =1 h h−1 h
In this paper, we will prove the fractional forms of the classical Hardy, Copson type and its reversed and Leindler inequalities with employing conformable calculus on time scales
The article is structured as follows: Section 2 is an introduction of the basics of fractional calculus on timescales and Section 3 contains the main results
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affill =1 l l. Bennett in [7,8] established a converses of the inequalities (3) and (4) He exemplified that if m ≤ 0 < h < 1, :. In the same paper [25], Saker et al proved the time scale transcript of the BennetLeindler inequalities (9) and (10), respectively, as follows: Assume that T is a time scale. Very recently Torres and others, in [31,32], combined a time scale calculus and conformable calculus and obtained the new fractional calculus on timescales. In this paper, we will prove the fractional forms of the classical Hardy, Copson type and its reversed and Leindler inequalities with employing conformable calculus on time scales. The article is structured as follows: Section 2 is an introduction of the basics of fractional calculus on timescales and Section 3 contains the main results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
