On some Hardy-type inequalities for fractional calculus operators

2017 ◽  
Vol 11 (2) ◽  
pp. 438-457 ◽  
Author(s):  
Sajid Iqbal ◽  
Josip Pečarić ◽  
Muhammad Samraiz ◽  
Zivorad Tomovski
Keyword(s):  
Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Fractional Calculus Operators

scholarly journals ON A CLASS OF FRACTIONAL HARDY-TYPE INEQUALITIES

Fractals ◽  
2021 ◽  
pp. 2240011
Author(s):  
SHANHE WU ◽  
MUHAMMAD SAMRAIZ ◽  
SAJID IQBAL ◽  
GAUHAR RAHMAN
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Operators ◽  
Hilfer Fractional Derivative ◽  
Derivative Operator ◽  
Hardy Type Inequalities ◽  
New Class ◽  
Hardy Type ◽  
Fractional Calculus Operators

In this paper, we study a new class of Hardy-type inequalities involving fractional calculus operators. We derive the Hardy-type inequalities for the variant of Riemann–Liouville fractional calculus operators and [Formula: see text]-Hilfer fractional derivative operator. The obtained inequalities involving fractional operators are more general as compared to some existing results in the literature.

scholarly journals Weighted Hardy-type inequalities involving fractional calculus operators

2018 ◽  
Vol 534 (22) ◽  
pp. 77-91
Author(s):  
Sajid Iqbal ◽  
Josip Pečarić ◽  
Muhammad Samraiz ◽  
Živorad Tomovski
Keyword(s):  
Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Fractional Calculus Operators

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 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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