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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Kragujevac, Faculty of Technical Sciences Čačak
2024-01-01
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| Series: | Mathematica Moravica |
| Subjects: | |
| Online Access: | https://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2024/1450-59322402017M.pdf |
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| Summary: | 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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| ISSN: | 1450-5932 2560-5542 |