Some generalizations of dynamic Opial-type inequalities in conformable calculus

Fatma M. Khamis; M. M.A. El-Sheikh; Thabet Abdeljawad; Aiman Mukheimer; Gamal A.F. Ismail

doi:10.1186/s13660-024-03224-z

Some generalizations of dynamic Opial-type inequalities in conformable calculus

Fatma M. Khamis^*
, M. M.A. El-Sheikh
, Thabet Abdeljawad
, Aiman Mukheimer
, Gamal A.F. Ismail

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on Hölder’s inequality, some algebraic inequalities, and a simple consequence of Keller’s chain rule on time scales. Our obtained results unify and extend some continuous and discrete inequalities. In the special case α=1, our results cover some well-known inequalities of Opial-type on time scales.

Original language	English
Article number	152
Journal	Journal of Inequalities and Applications
Volume	2024
Issue number	1
DOIs	https://doi.org/10.1186/s13660-024-03224-z
Publication status	Published - Dec 2024
Externally published	Yes

Keywords

Conformable fractional calculus
Dynamic inequality
Hölder inequality
Opial-type inequality

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10.1186/s13660-024-03224-z

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title = "Some generalizations of dynamic Opial-type inequalities in conformable calculus",

abstract = "In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on H{\"o}lder{\textquoteright}s inequality, some algebraic inequalities, and a simple consequence of Keller{\textquoteright}s chain rule on time scales. Our obtained results unify and extend some continuous and discrete inequalities. In the special case α=1, our results cover some well-known inequalities of Opial-type on time scales.",

keywords = "Conformable fractional calculus, Dynamic inequality, H{\"o}lder inequality, Opial-type inequality",

author = "Khamis, \{Fatma M.\} and El-Sheikh, \{M. M.A.\} and Thabet Abdeljawad and Aiman Mukheimer and Ismail, \{Gamal A.F.\}",

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doi = "10.1186/s13660-024-03224-z",

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AU - Khamis, Fatma M.

AU - El-Sheikh, M. M.A.

AU - Abdeljawad, Thabet

AU - Mukheimer, Aiman

AU - Ismail, Gamal A.F.

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/12

Y1 - 2024/12

N2 - In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on Hölder’s inequality, some algebraic inequalities, and a simple consequence of Keller’s chain rule on time scales. Our obtained results unify and extend some continuous and discrete inequalities. In the special case α=1, our results cover some well-known inequalities of Opial-type on time scales.

AB - In this paper, we consider generalized conformable integrals to establish new Opial-type inequalities. The obtained results mainly depend on Hölder’s inequality, some algebraic inequalities, and a simple consequence of Keller’s chain rule on time scales. Our obtained results unify and extend some continuous and discrete inequalities. In the special case α=1, our results cover some well-known inequalities of Opial-type on time scales.

KW - Conformable fractional calculus

KW - Dynamic inequality

KW - Hölder inequality

KW - Opial-type inequality

UR - https://www.scopus.com/pages/publications/85211189172

U2 - 10.1186/s13660-024-03224-z

DO - 10.1186/s13660-024-03224-z

M3 - Article

AN - SCOPUS:85211189172

SN - 1025-5834

VL - 2024

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 152

ER -

Some generalizations of dynamic Opial-type inequalities in conformable calculus

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Keywords

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