  In this paper, we introduce the concept of the $\alpha$-fractal function and
fractal approximation for a set-valued continuous map defined on a closed and
bounded interval of real numbers. Also, we study some properties of such
fractal functions. Further, we estimate the perturbation error between the
given continuous function and its $\alpha$-fractal function. Additionally, we
define a new graph of a set-valued function different from the standard graph
introduced in the literature and establish some bounds on the fractal dimension
of the newly defined graph of some special classes of set-valued functions.
Also, we explain the need to define this new graph with examples. In the
sequel, we prove that this new graph of an $\alpha$-fractal function is an
attractor of an iterated function system.
