On the quantum theory of the natural transform and some applications. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Al-Omari, Shrideh K. Q.
• Is Part Of: Journal of difference equations and applications. Volume 25:Issue 1(2019)
• Page Start: 21
• Page End: 37
• Publication Date: 2019-01-02
• Subjects: q-Laplace transform -- q-natural transform -- q-Bessel function -- Fox's Hq-functions; 26A33; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2018.1554063
• Languages: English
• ISSNs: 1023-6198

Abstract

ABSTRACT: This article deals with definitions and applications of the q -theory of the Natural transform to various classes of special functions. We discuss q -analogues of the Natural transform on various classes of q -hypergeometric functions, q -Bessel functions, q -gamma functions, q -exponential functions, q -sine functions, q -cosine functions and some polynomials of certain growth conditions. Moreover, we derive results involving certain Fox'sH q -functions. Over and above, we introduce various examples and corollaries to show effectiveness and generality of the obtained results as well.