Basic results for fractional anisotropic spaces and applications: Basic results for fractional anisotropic spaces and applications
In this paper, we introduce a new space that generalizes the ϕ -Hilfer space with the ξ ( · ) -Laplacian operator, denoted ( ϕ , ξ ( · ) ) -HFDS. We refer to this new space as the ϕ -fractional space with anisotropic ξ → ( · ) -Laplacian operator, abbreviated as ( ϕ , ξ → ( · ) ) -HFDAS. We prove th...
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| Veröffentlicht in: | Journal of pseudo-differential operators and applications 2024-12, Vol.15 (4), Article 71 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we introduce a new space that generalizes the
ϕ
-Hilfer space with the
ξ
(
·
)
-Laplacian operator, denoted
(
ϕ
,
ξ
(
·
)
)
-HFDS. We refer to this new space as the
ϕ
-fractional space with anisotropic
ξ
→
(
·
)
-Laplacian operator, abbreviated as
(
ϕ
,
ξ
→
(
·
)
)
-HFDAS. We prove that
(
ϕ
,
ξ
→
(
·
)
)
-HFDAS is a separable, and reflexive Banach space. Furthermore, we extend some well-known properties and embedding results of the
(
ϕ
,
ξ
(
·
)
)
-HFDS space to
(
ϕ
,
ξ
→
(
·
)
)
-HFDAS. Moreover, we illustrate an application of
(
ϕ
,
ξ
→
(
·
)
)
-HFDAS by solving a differential equation via variational methods. |
|---|---|
| ISSN: | 1662-9981 1662-999X |
| DOI: | 10.1007/s11868-024-00641-y |