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

Abstract

Abstract 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.

Keywords

• q-Laplace transform
• q-Natural transform
• q-Bessel function
• Fox’s q-H-functions