Q-Laplace transforms

Abstract

Two q-analogues of the well-known Laplace transform are defined with the help of the Jackson integral. In this paper, firstly q-convolution theorem for qLs operator is studied. Some convolution examples are obtained and also qLsxa-1f(x) = S qLsxa Σ∞i=0 qα f (q ix), α > 0 is proved via q-convolution theorem. qLsxaf (x) is found for some elementary functions. Finally, qLsLqLsx nDq(m)f (x) is obtained in terms of qLs,f (x). Furthermore, qStf (x) and,qSt f (x) are defined and some properties of qSt f (x) and qStα f (x) are proved.