On the $q$-analogue of Duhamel's principle
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910053664030720 |
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| author | Sebih, Mohammed Elamine Shaimardan, Serikbol Ali, Irfan |
| author_facet | Sebih, Mohammed Elamine Shaimardan, Serikbol Ali, Irfan |
| contents | In this paper, we revisit the classical Duhamel's principle and provide a self-contained proof of this fundamental tool for linear evolution equations and systems of coupled equations. Moreover, we establish a $q$-analogue of Duhamel's principle for $q$-evolution equations of order $k\geq 1$ generated by Jackson's $q$-difference operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14274 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $q$-analogue of Duhamel's principle Sebih, Mohammed Elamine Shaimardan, Serikbol Ali, Irfan Analysis of PDEs 34A99, 05A30, 33D05 In this paper, we revisit the classical Duhamel's principle and provide a self-contained proof of this fundamental tool for linear evolution equations and systems of coupled equations. Moreover, we establish a $q$-analogue of Duhamel's principle for $q$-evolution equations of order $k\geq 1$ generated by Jackson's $q$-difference operator. |
| title | On the $q$-analogue of Duhamel's principle |
| topic | Analysis of PDEs 34A99, 05A30, 33D05 |
| url | https://arxiv.org/abs/2603.14274 |