\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ H_{M+1N}^{m,n+1}\left[ \lambda \dfrac{u^{k}}{v^{k}};q\left\vert 
\begin{array}{l}
\left( -\lambda ,k\right) ,...,\left( a_{M},\alpha _{M}\right) \\ 
\left( b_{1},\beta _{1}\right) ,...,\left( b_{N},\beta _{N}\right)\end{array}\right. \right] .$

$\left( \mathtt{ii}\right) $ *Let* $\lambda $* be any complex number and* $k\in \left( -\infty ,0\right) .$* The* $q$*-Natural transform* $N_{q}$* of the Fox’s* $H_{q}$*-Function is given as*

$N_{q}\left( x^{\lambda }H_{M,N}^{m,n}\left[ \lambda x^{k};q\left\vert 
\begin{array}{l}
\left( a_{1},\alpha _{1}\right) ,\left( a_{1},\alpha _{1}\right) ...,\left(
a_{M},\alpha _{M}\right) \\ 
\left( b_{1},\beta _{1}\right) ,b_{2},...,\left( b_{N},\beta _{N}\right)\end{array}\right. \right] \right) \left( u;v\right) =\dfrac{u^{\lambda }}{v^{\lambda
+1}G\left( q\right) }$

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