On q-analogues of the natural transform of certain q-Bessel functions and some application

Abstract

Theory and applications of q-integral transforms have been evolving rapidly over the recent years. Consequently, several q-analogues of certain classical integrals have been investigated by many authors in various citations. In this paper, we give the q-analogues of the Natural transform and we apply further the resulting analogues to three families of q-Bessel functions. Results of this paper are new and complement previously known results in this theory. Moreover, we give some examples to show effectiveness of the proposed results in case of q-Sumudu and q-Laplace transforms.