On the quantum theory of the natural transform and some applications

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's $H_q$-functions. Over and above, we introduce various examples and corollaries to show effectiveness and generality of the obtained results as well.

KEYWORDS:

• q-Laplace transform
• q-natural transform
• q-Bessel function
• Fox's $H_q$-functions

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 26A33

Acknowledgments

The authors would like to express many thanks to the anonymous referees for their corrections and comments on this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.