Some results for Laplace-type integral operator in quantum calculus

Abstract

In the present article, we wish to discuss q-analogues of Laplace-type integrals on diverse types of q-special functions involving Fox's H-q-functions. Some of the discussed functions are the q-Bessel functions of the first kind, the q-Bessel functions of the second kind, the q-Bessel functions of the third kind, and the q-Struve functions as well. Also, we obtain some associated results related to q-analogues of the Laplace-type integral on hyperbolic sine (cosine) functions and some others of exponential order type as an application to the given theory.