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We study a q-analog of a singularly perturbed Cauchy problem with irregular singularityin the complex domain which generalizes a previous result by Malek in (2011). First, we construct solutions defined in open q-spirals to the origin. By means of a q-Gevrey version of Malgrange-Sibuya theorem we show the existence of a formal power series in the perturbation parameter which turns out to be the q-Gevrey asymptotic expansion (of certain type) of the actual solutions

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On<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-Gevrey Asymptotics for Singularly Perturbed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-Difference-Differential Problems with an Irregular Singularity

Onq-Gevrey Asymptotics for Singularly Perturbedq-Difference-Differential Problems with an Irregular Singularity