as$$\begin{aligned}
_{r}\phi _{s}\left[ \left. 
\begin{array}{c}
a_{1},a_{2},...,a_{r} \\ 
b_{1},b_{2},...,b_{s}\end{array}\right\vert q,z\right] &=&\sum_{0}^{\infty }\frac{\left(
a_{1},a_{2},...,a_{r};q\right) _{n}}{\left( b_{1},b_{2},...,b_{s};q\right)
_{n}}\frac{z^{n}}{\left( q;q\right) _{n}}  \TCItag{13} \\
&&\text{and}  \notag \\
_{m-k}\Phi _{m-1}\left[ \left. 
\begin{array}{c}
a_{1},a_{2},...,a_{m-k} \\ 
b_{1},b_{2},...,b_{m-1}\end{array}\right\vert q,z\right] &=&\sum_{0}^{\infty }\frac{\left(
a_{1},...,a_{m-k};q\right) _{n}}{\left( b_{1},...,b_{m-1};q\right) _{n}}\left[ \left( -1\right) ^{n}q^{\binom{n}{2}}\right] ^{k}\frac{z^{n}}{\left(
q;q\right) _{n}},  \notag \\
&&  \TCItag{14}\end{aligned}$$where $\left( a_{1},a_{2},...,a_{p};q\right) _{n}=\prod\limits_{0}^{p}\left(
a_{k},q\right) _{n}.$

For $\left\vert z\right\vert <2$, some $q$-analogues of the Bessel function are defined as$$\begin{aligned}
J_{v}^{\left( 1\right) }\left( z;q\right) &=&\frac{\left( q^{v+1};q\right)
_{\infty }}{\left( q;q\right) _{\infty }}\left( \frac{z}{2}\right)
^{2}{}_{2}\Phi _{1}\left[ \left. 
\begin{array}{cc}
0 & 0 \\ 
q^{v+1} & 
\end{array}\right\vert q,\frac{-z^{2}}{2}\right] =\left( \frac{z}{2}\right)
^{v}\sum_{n=0}^{\infty }\frac{\left( \frac{-z^{2}}{4}\right) ^{n}}{\left(
q;q\right) _{v+n}}\left( q;q\right) _{n},  \notag \\
&&  \TCItag{15}\end{aligned}$$$$J_{v}^{\left( 2\right) }\left( z;q\right) =\tfrac{\left( q^{v+1};q\right)
_{\infty }}{\left( q;q\right) _{\infty }}\left( \tfrac{z}{2}\right) ^{v}\text{ }_{0}\Phi _{1}\left[ q^{v+1}\left\vert q,\frac{-q^{v+1}z^{2}}{4}\right. \right] =\left( \tfrac{z}{2}\right) ^{v}\sum_{0}^{\infty }\dfrac{q^{n\left( n+v\right) }}{\left( q;q\right) _{v+n}\left( q;q\right) _{n}}\left( \frac{-z^{2}}{4}\right) ^{n},  \tag{16}$$$$J_{v}^{\left( 3\right) }\left( z;q\right) =\frac{\left( q^{v+1};q\right)
_{\infty }}{\left( q;q\right) _{\infty }}z^{v}{}_{1}\Phi _{1}\left[ \left. 
\begin{array}{c}
0 \\ 
q^{v+1}\end{array}\right\vert q,qz^{2}\right] =z^{v}\sum_{0}^{\infty }\frac{\left( -1\right)
^{n}q^{\frac{n\left( n-1\right) }{2}}}{\left( q;q\right) _{v+n}\left(
q;q\right) _{n}}\text{ }.\text{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }  \tag{17}$$

The $q$-Analogues of the Natural Transform
==========================================

Theory and applications of $q$-integral transforms are evolving rapidly over the recent years. Since Jackson $[11]$ presented 