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

[摘要] 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.

[学科分类] 电力

[关键词] q -Laplace transform;q -Natural transform;q -Bessel function;Fox’s q - H -functions