q -Analogues and properties of the Laplace-type integral operator in the quantum calculus theory

@article{AlOmari2020qA,
title={q -Analogues and properties of the Laplace-type integral operator in the quantum calculus theory},
author={S. Al-Omari},
journal={Journal of Inequalities and Applications},
year={2020},
volume={2020},
pages={1-14}
}

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.