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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University of Kragujevac, Faculty of Technical Sciences Čačak
2024-01-01
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| 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. |
| format | Article |
| id | doaj-art-3878f737f75649888890e97796774ee0 |
| institution | Kabale University |
| issn | 1450-5932 2560-5542 |
| 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 |
| work_keys_str_mv | AT mirkovictatjana opialinequalitiesforaconformablefractionalcalculusontimescales AT bajictatjana opialinequalitiesforaconformablefractionalcalculusontimescales |