On the quantum theory of the natural transform and some applications. Issue 1 (2nd January 2019) - Al-Omari, Shrideh K. Q.
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.