  Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic
operations of a Burgin type is applicable to all fractals whose cardinality is
continuum. The resulting definitions of derivatives and integrals are simpler
from what one finds in the more traditional literature of the subject, and they
often work in the cases where the standard methods fail. As an illustration, we
perform a Fourier transform of a real-valued function with Sierpi\'nski-set
domain. The resulting formalism is as simple as the usual undergraduate
calculus.
