New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales

Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math><...

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Autores principales:	Ahmed A. El-Deeb, Hijaz Ahmad, Jan Awrejcewicz
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Steffensen’s inequality dynamic inequality α-conformable calculus time scale Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3de11f4e239944e5b1ca8714b0416f71
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spelling	oai:doaj.org-article:3de11f4e239944e5b1ca8714b0416f712021-11-25T19:06:20ZNew Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales10.3390/sym131120492073-8994https://doaj.org/article/3de11f4e239944e5b1ca8714b0416f712021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2049https://doaj.org/toc/2073-8994Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable dynamic inequalities of Steffensen-type on time scales. In the case when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we obtain some well-known time scale inequalities due to Steffensen inequalities. For some specific time scales, we further show some relevant inequalities as special cases: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable integral inequalities and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.Ahmed A. El-DeebHijaz AhmadJan AwrejcewiczMDPI AGarticleSteffensen’s inequalitydynamic inequalityα-conformable calculustime scaleMathematicsQA1-939ENSymmetry, Vol 13, Iss 2049, p 2049 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Steffensen’s inequality dynamic inequality α-conformable calculus time scale Mathematics QA1-939
spellingShingle	Steffensen’s inequality dynamic inequality α-conformable calculus time scale Mathematics QA1-939 Ahmed A. El-Deeb Hijaz Ahmad Jan Awrejcewicz New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales
description	Building on the work of Josip Pečarić in 2013 and 1982 and on the work of Srivastava in 2017. We prove some new <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable dynamic inequalities of Steffensen-type on time scales. In the case when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, we obtain some well-known time scale inequalities due to Steffensen inequalities. For some specific time scales, we further show some relevant inequalities as special cases: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable integral inequalities and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-conformable discrete inequalities. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.
format	article
author	Ahmed A. El-Deeb Hijaz Ahmad Jan Awrejcewicz
author_facet	Ahmed A. El-Deeb Hijaz Ahmad Jan Awrejcewicz
author_sort	Ahmed A. El-Deeb
title	New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales
title_short	New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales
title_full	New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales
title_fullStr	New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales
title_full_unstemmed	New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales
title_sort	new fractional dynamic inequalities via conformable delta derivative on arbitrary time scales
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3de11f4e239944e5b1ca8714b0416f71
work_keys_str_mv	AT ahmedaeldeeb newfractionaldynamicinequalitiesviaconformabledeltaderivativeonarbitrarytimescales AT hijazahmad newfractionaldynamicinequalitiesviaconformabledeltaderivativeonarbitrarytimescales AT janawrejcewicz newfractionaldynamicinequalitiesviaconformabledeltaderivativeonarbitrarytimescales
_version_	1718410272225361920

New Fractional Dynamic Inequalities via Conformable Delta Derivative on Arbitrary Time Scales

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