  In contrast to the univariate case, several definitions are available for the
notion of bounded variation for a bivariate function. This article is an
attempt to study the Hausdorff dimension and box dimension of the graph of a
continuous function defined on a rectangular region in R2, which is of bounded
variation according to some of these approaches. We show also that the
Riemann-Liouville fractional integral of a function of bounded variation in the
sense of Arzela is of bounded variation in the same sense. Further, we deduce
the Hausdorff dimension and box dimension of the graph of the fractional
integral of a bivariate continuous function of bounded variation.
