  A Fokker Planck equation on fractal curves is obtained, starting from
Chapmann-Kolmogorov equation on fractal curves. This is done using the recently
developed calculus on fractals, which allows one to write differential
equations on fractal curves. As an important special case, the diffusion and
drift coefficients are obtained, for suitable transition probability to get the
diffusion equation on fractal curves. This equation is of first order in time,
and, in space variable it involves derivatives of order $\alpha$, $\alpha$
being the dimension of the curve. The solution of this equation with localized
initial condition shows deviation from ordinary diffusion behaviour due to
underlying fractal space in which diffusion is taking place. An exact solution
of this equation manifests a subdiffusive behaviour. The dimension of the
fractal path can be estimated from the distrubution function.
