Opial inequalities for a conformable ∆-fractional calculus on time scales

In this paper, an Opial-type inequality is introduced on time scale for a conformal ∆-fractional differentiable function of order a, a ∈ (0, 1]. In the case where the certain weight functions are included, one generalization of the Opial inequality is proved using conformal ∆-fractional calculus on...

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Main Authors: Mirković Tatjana, Bajić Tatjana
Format: Article
Language:English
Published: University of Kragujevac, Faculty of Technical Sciences Čačak 2024-01-01
Series:Mathematica Moravica
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Online Access:https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2024/1450-59322402017M.pdf
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author Mirković Tatjana
Bajić Tatjana
author_facet Mirković Tatjana
Bajić Tatjana
author_sort Mirković Tatjana
collection DOAJ
description In this paper, an Opial-type inequality is introduced on time scale for a conformal ∆-fractional differentiable function of order a, a ∈ (0, 1]. In the case where the certain weight functions are included, one generalization of the Opial inequality is proved using conformal ∆-fractional calculus on time scales. Moreover, for n times conformal ∆-fractional differentiable function on time scale, n ∈ N, an Opial inequality is obtained. In particular, through examples, the main results from the paper are compared with classical ones on generalized time scales. At the end of the paper, we indicate possible applications of the obtained Opial-type inequalities in the consideration of stochastic dynamical equations where conformal ∆-fractional calculus on time scales is included, which requires further research.
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language English
publishDate 2024-01-01
publisher University of Kragujevac, Faculty of Technical Sciences Čačak
record_format Article
series Mathematica Moravica
spelling doaj-art-3878f737f75649888890e97796774ee02025-01-08T16:28:21ZengUniversity of Kragujevac, Faculty of Technical Sciences ČačakMathematica Moravica1450-59322560-55422024-01-01282173210.5937/MatMor2402017M1450-59322402017MOpial inequalities for a conformable ∆-fractional calculus on time scalesMirković Tatjana0Bajić Tatjana1Academy of Applied Studies Šabac, Department of Medical and Business-Technological Studies, Šabac, SerbiaUniversity of Belgrade, Faculty of Mathematics, Belgrade, SerbiaIn this paper, an Opial-type inequality is introduced on time scale for a conformal ∆-fractional differentiable function of order a, a ∈ (0, 1]. In the case where the certain weight functions are included, one generalization of the Opial inequality is proved using conformal ∆-fractional calculus on time scales. Moreover, for n times conformal ∆-fractional differentiable function on time scale, n ∈ N, an Opial inequality is obtained. In particular, through examples, the main results from the paper are compared with classical ones on generalized time scales. At the end of the paper, we indicate possible applications of the obtained Opial-type inequalities in the consideration of stochastic dynamical equations where conformal ∆-fractional calculus on time scales is included, which requires further research.https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2024/1450-59322402017M.pdfopial inequalityconformable ∆-fractional differentiable functiontime scale
spellingShingle Mirković Tatjana
Bajić Tatjana
Opial inequalities for a conformable ∆-fractional calculus on time scales
Mathematica Moravica
opial inequality
conformable ∆-fractional differentiable function
time scale
title Opial inequalities for a conformable ∆-fractional calculus on time scales
title_full Opial inequalities for a conformable ∆-fractional calculus on time scales
title_fullStr Opial inequalities for a conformable ∆-fractional calculus on time scales
title_full_unstemmed Opial inequalities for a conformable ∆-fractional calculus on time scales
title_short Opial inequalities for a conformable ∆-fractional calculus on time scales
title_sort opial inequalities for a conformable ∆ fractional calculus on time scales
topic opial inequality
conformable ∆-fractional differentiable function
time scale
url https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2024/1450-59322402017M.pdf
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