On a novel fractional Caputo-derivative Orlicz space
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916345994543104 |
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| author | Ayoub, Kasmi Houssine, Azroul El Mohammed, Shimi |
| author_facet | Ayoub, Kasmi Houssine, Azroul El Mohammed, Shimi |
| contents | In this work, we aim to explore whether a novel type of fractional space can be defined using Orlicz spaces and fractional calculus. This inquiry is fruitful, as extending classical results to new contexts can lead to a better and deeper understanding of those classical results. Our main objective is to introduce a new fractional Caputo-derivative Orlicz space, denoted by $\mathcal{O}^{α,G}(Λ, \mathbb{R}) $. We are interested in several qualitative properties of this space, such as reflexivity, completeness, and separability. Additionally, we establish a continuous embedding results of this space into a suitable Orlicz space and the space of continuous functions. As an application, we use the mountain-pass theorem (MPT) to ensure the existence of a nontrivial weak solution for a new class of fractional-type problems in Orlicz space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a novel fractional Caputo-derivative Orlicz space Ayoub, Kasmi Houssine, Azroul El Mohammed, Shimi Functional Analysis Analysis of PDEs 46E30, 46E35, 35R11, 35A15 In this work, we aim to explore whether a novel type of fractional space can be defined using Orlicz spaces and fractional calculus. This inquiry is fruitful, as extending classical results to new contexts can lead to a better and deeper understanding of those classical results. Our main objective is to introduce a new fractional Caputo-derivative Orlicz space, denoted by $\mathcal{O}^{α,G}(Λ, \mathbb{R}) $. We are interested in several qualitative properties of this space, such as reflexivity, completeness, and separability. Additionally, we establish a continuous embedding results of this space into a suitable Orlicz space and the space of continuous functions. As an application, we use the mountain-pass theorem (MPT) to ensure the existence of a nontrivial weak solution for a new class of fractional-type problems in Orlicz space. |
| title | On a novel fractional Caputo-derivative Orlicz space |
| topic | Functional Analysis Analysis of PDEs 46E30, 46E35, 35R11, 35A15 |
| url | https://arxiv.org/abs/2408.01842 |