Fractal calculus on [0, 1]

Ordinary differential equations are generalized to fractal supports with regular or multifractal properties. This can be done by considering the corresponding integral equations with respect to the measure. Closed form solutions of simple differential equations (giving rise to exponential, sine and cosine functions) on fractals are presented and the generalization to arbitrary differential equations discussed. Some applications of this formalism are presented in connection with multifractality.