Abstract
In this article, we prove some new fractional dynamic inequalities on time scales via conformable calculus. By using chain rule and Hölder’s inequality on timescales we establish the main results. When α = 1 we obtain some well-known time-scale inequalities due to Hardy, Copson, Bennett and Leindler inequalities.
Highlights
Hardy [2], by using the calculus of variations, proved the continuous inequality of (1) which has the form
The new fractional calculus on timescales is presented with applications to some new fractional inequalities on timescales like Hardy, Bennett, Copson and Leindler types
The technique is based on the applications of well-known inequalities and new tools from fractional calculus
Summary
Hardy [2], by using the calculus of variations, proved the continuous inequality of (1) which has the form The integral versions of the inequalities (10) and (11) was proved by Copson in [10] The main question that arises now is: Is it possible to prove new fractional inequalities on timescales and give a unified approach of such studies?
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