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

Abstract

The main objective of the present article is to prove some new ∇ 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 (γ,a)-nabla conformable Hölder’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.

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

“…Now, as a new result, we are interested in discussing the inequality (24) in the case of the extrema of integration η a θ(s)∆s being replaced to be from η to ∞. In fact, that is what we will do in the following theorem.…”

“…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. ).…”

On Some Important Class of Dynamic Hilbert’s-Type Inequalities on Time Scales

“…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].…”

On Some Important Dynamic Inequalities of Hardy–Hilbert-Type on Timescales

“…Over the past decade, a great number of dynamic Hilbert-type inequalities on timescales has been established by many researchers who were motivated by some applications, see the papers [5][6][7][8][9][10][11][12][13][14][15][16][17].…”