Generalizations of some important fractional integral inequalities by using a parameter

Fatih Hezenci; Hüseyin Budak; Hasan Kara; Praveen Agarwal

doi:10.1016/B978-0-44-318505-2.00008-8

Generalizations of some important fractional integral inequalities by using a parameter

Fatih Hezenci
, Hüseyin Budak
, Hasan Kara
, Praveen Agarwal

Nonlinear Dynamic Research Centre (NDRC)

Duzce University
International College of Engineering
International Telematic University Uninettuno

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In the present paper, we first prove an equality for the functions whose second derivatives in absolute value are convex. By using this equality we obtain some parameterized inequalities for twice differentiable functions by using generalized fractional integrals. Finally, we show that our main results reduce to trapezoid, midpoint, and Simpson- and Bullen-type inequalities proved in earlier papers.

Original language	English
Title of host publication	Recent Trends in Fractional Calculus and its Applications
Publisher	Elsevier
Pages	21-37
Number of pages	17
ISBN (Electronic)	9780443185052
ISBN (Print)	9780443185069
DOIs	https://doi.org/10.1016/B978-0-44-318505-2.00008-8
State	Published - 1 Jan 2024

Keywords

Bullen-type inequalities
Generalized fractional integrals
Midpoint inequalities
Simpson-type inequalities
Trapezoid inequalities
Twice differentiable functions

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10.1016/B978-0-44-318505-2.00008-8

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AU - Budak, Hüseyin

AU - Kara, Hasan

AU - Agarwal, Praveen

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N2 - In the present paper, we first prove an equality for the functions whose second derivatives in absolute value are convex. By using this equality we obtain some parameterized inequalities for twice differentiable functions by using generalized fractional integrals. Finally, we show that our main results reduce to trapezoid, midpoint, and Simpson- and Bullen-type inequalities proved in earlier papers.

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KW - Bullen-type inequalities

KW - Generalized fractional integrals

KW - Midpoint inequalities

KW - Simpson-type inequalities

KW - Trapezoid inequalities

KW - Twice differentiable functions

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BT - Recent Trends in Fractional Calculus and its Applications

PB - Elsevier

ER -

Generalizations of some important fractional integral inequalities by using a parameter

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Keywords

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