  In this article, we study the novel concept of non-stationary iterated
function systems (IFSs) introduced by Massopust in 2019. At first, using a
sequence of different contractive operators, we construct non-stationary
$\alpha$-fractal functions on the space of all continuous functions. Next, we
provide some elementary properties of the fractal operator associated with the
nonstationary $\alpha$-fractal functions. Further, we show that the proposed
interpolant generalizes the existing stationary interpolant in the sense of
IFS. For a class of functions defined on an interval, we derive conditions on
the IFS parameters so that the corresponding non-stationary $\alpha$-fractal
functions are elements of some standard spaces like bounded variation space,
convex Lipschitz space, and other function spaces. Finally, we discuss the
dimensional analysis of the corresponding non-stationary $\alpha$-fractal
functions on these spaces.
