Existence and regularity results for space-time fractional integro-differential equation of Kirchhoff type with memory
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909169578147840 |
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| author | Kumar, Lalit Sista, Sivaji Ganesh Sreenadh, Konijeti |
| author_facet | Kumar, Lalit Sista, Sivaji Ganesh Sreenadh, Konijeti |
| contents | This paper analyses a Kirchhoff type quasilinear space-time fractional integro-differential equation with memory $(\mathcal{K}^{s}_α)$. Various a priori bounds are derived in different norms on the solution of the considered equation. Utilizing these a priori bounds, existence and uniqueness of the weak solution to the proposed model are proved. Furthermore, regularity results on the solution of $(\mathcal{K}^{s}_α)$ are established. The contribution made in this work provides a framework for further investigation of such types of partial integro-differential equation $(\mathcal{K}^{s}_α)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and regularity results for space-time fractional integro-differential equation of Kirchhoff type with memory Kumar, Lalit Sista, Sivaji Ganesh Sreenadh, Konijeti Analysis of PDEs 35K55, 35R11, 47G20, 35B44, 35Q91 This paper analyses a Kirchhoff type quasilinear space-time fractional integro-differential equation with memory $(\mathcal{K}^{s}_α)$. Various a priori bounds are derived in different norms on the solution of the considered equation. Utilizing these a priori bounds, existence and uniqueness of the weak solution to the proposed model are proved. Furthermore, regularity results on the solution of $(\mathcal{K}^{s}_α)$ are established. The contribution made in this work provides a framework for further investigation of such types of partial integro-differential equation $(\mathcal{K}^{s}_α)$. |
| title | Existence and regularity results for space-time fractional integro-differential equation of Kirchhoff type with memory |
| topic | Analysis of PDEs 35K55, 35R11, 47G20, 35B44, 35Q91 |
| url | https://arxiv.org/abs/2404.09328 |