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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.15972 |
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| _version_ | 1866911325339254784 |
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| author | Kasmi, Ayoub Azroul, El Houssine Shimi, Mohammed |
| author_facet | Kasmi, Ayoub Azroul, El Houssine Shimi, Mohammed |
| contents | In this paper, we introduce and study a novel class of generalized $(Φ_x,ψ)$-fractional Musielak spaces $\mathcal{K}_{Φ_x}^{α, β, ψ}$, which extends classical fractional spaces and offers the flexibility to model heterogeneous and nonlinear phenomena with memory and nonlocal effects. A detailed and rigorous analysis of their functional structure is carried out. Several new properties and embedding results are established, highlighting the originality of the proposed framework and its relevance to nonlocal BVPs. To illustrate the significance of this functional setting, we prove the existence of nontrivial solutions to a nonlinear fractional differential problem under an Ambrosetti--Rabinowitz type condition, using the mountain pass theorem. Our results provide new perspectives for the analysis of nonlocal and nonhomogeneous equations in variable-exponent and Musielak-Orlicz settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental Properties and Embedding Results in a Novel $(Φ_x, ψ)$-Fractional Musielak Space with an Application to Nonlocal BVP Kasmi, Ayoub Azroul, El Houssine Shimi, Mohammed Analysis of PDEs In this paper, we introduce and study a novel class of generalized $(Φ_x,ψ)$-fractional Musielak spaces $\mathcal{K}_{Φ_x}^{α, β, ψ}$, which extends classical fractional spaces and offers the flexibility to model heterogeneous and nonlinear phenomena with memory and nonlocal effects. A detailed and rigorous analysis of their functional structure is carried out. Several new properties and embedding results are established, highlighting the originality of the proposed framework and its relevance to nonlocal BVPs. To illustrate the significance of this functional setting, we prove the existence of nontrivial solutions to a nonlinear fractional differential problem under an Ambrosetti--Rabinowitz type condition, using the mountain pass theorem. Our results provide new perspectives for the analysis of nonlocal and nonhomogeneous equations in variable-exponent and Musielak-Orlicz settings. |
| title | Fundamental Properties and Embedding Results in a Novel $(Φ_x, ψ)$-Fractional Musielak Space with an Application to Nonlocal BVP |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.15972 |