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arXiv · 2603.14274

On the $q$-analogue of Duhamel's principle

Mohammed Elamine Sebih·Serikbol Shaimardan·Irfan Ali
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Abstract

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.

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Mohammed Elamine Sebih, Serikbol Shaimardan, Irfan Ali. 2026-03-15. On the $q$-analogue of Duhamel's principle. https://arxiv.org/abs/2603.14274

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