Abstract
In this paper an application of the recently introduced pre-Lie Magnus expansion to Jackson’s q -integral and q -exponentials is presented. Twisted dendriform algebras, which are the natural algebraic framework for Jackson’s q -analogs, are introduced for that purpose. It is shown how the pre-Lie Magnus expansion is used to solve linear q -differential equations. We also briefly outline the theory of linear equations in twisted dendriform algebras.
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