Hahn Laplace transform and its applications

English (OpenAlex)

Abstract Like q q -calculus, Hahn calculus (or q , ω q,\omega -calculus) is constructed by defining a difference derivative operator and an integral operator. The q , ω q,\omega -analogs of the integral representations of the Laplace transform and related special functions, such as gamma and beta, are proposed in this article. Then, some basic properties similar to classical and q q -analogs are investigated. Finally, a few examples are given to solve q , ω q,\omega -initial value problems via the newly introduced q , ω q,\omega -Laplace transform.