English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study a $q-$analog of a singularly perturbed Cauchy problem with irregularsingularity in the complex domain which generalizes a previous result by S.Malek in \cite{malek}. First, we construct solutions defined in open$q-$spirals to the origin. By means of a $q-$Gevrey version of Malgrange-Sibuyatheorem we show the existence of a formal power series in the perturbationparameter which turns out to be the $q-$Gevrey asymptotic expansion (of certaintype) of the actual solutions.

On $q-$Gevrey asymptotics for singularly perturbed $q-$difference-differential problems with an irregular singularity