English

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 qq-analogue of Duhamel's principle for qq-evolution equations of order k1k\geq 1 generated by Jackson's qq-difference operator.

Keywords

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}
}