In this paper, we discuss the q-Laplace-type integral operator on certain class of special functions. We propose q-analogues and obtain results involving polynomials of even orders and functions of q-trigonometric types. Moreover, we establish results related to q-hyperbolic functions and certain q-differential operators. Relying on the given q-differentiation formulas, we finally derive the nth derivative of the q-Laplace-type integral and attain formulas including q-convolution products.

中文翻译：

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q-量子算术理论中Laplace型积分算子的模拟和性质

在本文中，我们讨论了关于某些特殊函数的q-Laplace型积分算子。我们提出q模拟，并获得涉及偶数阶和q三角函数的多项式的结果。此外，我们建立了与q双曲函数和某些q微分算子有关的结果。依靠给定的q微分公式，我们最终得出q-Laplace型积分的n阶导数，得到包括q卷积的公式。