On the $q$-analogue of Duhamel's principle
Analysis of PDEs
2026-03-17 v1
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 -analogue of Duhamel's principle for -evolution equations of order generated by Jackson's -difference operator.
Cite
@article{arxiv.2603.14274,
title = {On the $q$-analogue of Duhamel's principle},
author = {Mohammed Elamine Sebih and Serikbol Shaimardan and Irfan Ali},
journal= {arXiv preprint arXiv:2603.14274},
year = {2026}
}