Ordinary differential equations with fractal noise

The differential equation dx(t) = a(x(t); t) dZ(t) + b(x(t); t) dt for fractal-type functions Z(t) is determined via fractional calculus. Unde r appropriate conditions we prove existence and uniqueness of a local solut ion by means of its representation x(t) = h(y(t)+Z(t); t) for certain C-1-f unctions h and y. The method is also applied to Ito stochastic differential equations and leads to a general pathwise representation. Finally we discu ss fractal sample path properties of the solutions.