Hahn Laplace Transform and Its Applications

Abstract

Likeq-calculus, Hahn calculus (orq omega,-calculus) is constructed by defining a difference derivativeoperator and an integral operator. Theq omega,-analogs of the integral representations of the Laplace transformand related special functions, such as gamma and beta, are proposed in this article. Then, some basic proper-ties similar to classical andq-analogs are investigated. Finally, a few examples are given to solveq omega,-initialvalue problems via the newly introducedq omega,-Laplace transform.