On nabla conformable fractional Hardy-type inequalities on arbitrary time scales

Abstract

The main aim of the present article is to introduce some new ∇-conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini’s theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.

On Some Generalizations of Reverse Dynamic Hardy Type Inequalities on Time Scales

“…Additionally, by taking a look at the chain rule (23), we can say that there exists c ∈ [η, σ(η)] such that…”

“…For more details on Hardy-type inequalities and other types on time scales, we suggest [17][18][19][20][21][22][23][24][25][26][27][28][29] for the reader. ).…”

Hardy-Leindler-Type Inequalities via Conformable Delta Fractional Calculus

“…which are the time scale version for ( 5) and ( 6), respectively. For developing dynamic inequalities, see the papers ( [6][7][8][9][10][11]). Our target in this article is proving some fractional dynamic inequalities for Hardy-Leindler's type, and it is reversed with employing conformable calculus on time scales.…”

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“…Over the past decade, a great number of dynamic Hilbert-type inequalities on time scales have been established by many researchers who were motivated by some applications; see the papers [2][3][4][5][6][7][8][9][10][11][12][13]. For more details on time scales calculus, see [14].…”