  In this article, we investigate the fractal dimension of the graph of the
mixed Riemann-Liouville fractional integral for various choice of continuous
functions on a rectangular region. We estimate bounds for the box dimension and
the Hausdorff dimension of the graph of the mixed Riemann-Liouville fractional
integral of the functions which belong to the class of continuous functions and
the class of Holder continuous functions. We also show that the box dimension
of the graph of the mixed Riemann-Liouville fractional integral of
two-dimensional continuous functions is also two. Furthermore, we give
construction of unbounded variational continuous functions. Later, we prove
that the box dimension and the Hausdorff dimension of the graph of the mixed
Riemann-Liouville fractional integral of unbounded variational continuous
functions are also two.
