scholarly journals On some Hardy-type inequalities for generalized fractional integrals

2019 ◽  
pp. 33-54
Author(s):  
Muhammad Samraiz ◽  
Shafqat Shahzadi ◽  
Sajid Iqbal ◽  
Živorad Tomovski
Keyword(s):  
Fractional Integrals ◽  
Hardy Type Inequalities ◽  
Hardy Type

scholarly journals Some Hardy-Type Inequalities for Superquadratic Functions via Delta Fractional Integrals

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Usama Hanif ◽  
Ammara Nosheen ◽  
Rabia Bibi ◽  
Khuram Ali Khan ◽  
Hamid Reza Moradi
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Fractional Integrals ◽  
Discrete Fractional Calculus ◽  
Hardy Inequalities ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Superquadratic Functions

In this paper, Jensen and Hardy inequalities, including Pólya–Knopp type inequalities for superquadratic functions, are extended using Riemann–Liouville delta fractional integrals. Furthermore, some inequalities are proved by using special kernels. Particular cases of obtained inequalities give us the results on time scales calculus, fractional calculus, discrete fractional calculus, and quantum fractional calculus.

scholarly journals GENERALIZED MULTIVARIATE PRABHAKAR TYPE FRACTIONAL INTEGRALS AND INEQUALITIES

2021 ◽  
Vol 12 (4) ◽  
pp. 1-15
Author(s):  
GEORGE A. ANASTASSIOU
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Fractional Integrals ◽  
Hardy Type Inequalities ◽  
Basic Properties ◽  
Hardy Type ◽  
Left And Right

We introduce here the mixed generalized multivariate Prabhakar type left and right fractional integrals and study their basic properties, such as preservation of continuity and their boundedness as positive linear operators. Then we produce an interesting variety of related multivariate left and right fractional Hardy type inequalities under convexity. We introduce also other related multivariate fractional integrals

On refined Hardy-type inequalities with fractional integrals and fractional derivatives

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
Sajid Iqbal ◽  
Kristina Himmelreich ◽  
Josip Pečarić
Keyword(s):  
Fractional Derivatives ◽  
Fractional Integrals ◽  
Hardy Type Inequalities ◽  
Hardy Type

AbstractThe aim of this paper is to present new more general Hardy-type inequalities for different kinds of fractional integrals and fractional derivatives.

scholarly journals SOME HARDY-TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA DELTA FRACTIONAL INTEGRALS

Fractals ◽  
2021 ◽  
pp. 2240004
Author(s):  
FUZHANG WANG ◽  
USAMA HANIF ◽  
AMMARA NOSHEEN ◽  
KHURAM ALI KHAN ◽  
HIJAZ AHMAD ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Convex Functions ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Discrete Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Hilbert Type

In this paper, some Jensen- and Hardy-type inequalities for convex functions are extended by using Riemann–Liouville delta fractional integrals. Further, some Pólya–Knopp-type inequalities and Hardy–Hilbert-type inequality for convex functions are also proved. Moreover, some related inequalities are proved by using special kernels. Particular cases of resulting inequalities provide the results on fractional calculus, time scales calculus, quantum fractional calculus and discrete fractional calculus.

scholarly journals Some new Hardy-type inequalities on time scales

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmed A. El-Deeb ◽  
Hamza A. Elsennary ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hardy Type Inequalities ◽  
Hardy Type

On Hardy-Type Inequalities

1998 ◽  
Vol 194 (1) ◽  
pp. 23-33 ◽  
Author(s):  
D. E. Edmunds ◽  
R. Hurri-Syrjänen
Keyword(s):  
Hardy Type Inequalities ◽  
Hardy Type
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