Hahn Laplace transform and its applications

Hıra F.

DEMONSTRATIO MATHEMATICA, vol.56, no.1, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1515/dema-2023-0259
  • Journal Name: DEMONSTRATIO MATHEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Ondokuz Mayıs University Affiliated: Yes

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.