A new type of derivative is introduced, whose order of differentiation is itself a dynamical variable. The order can be a continuous variable depending on the dependent x or independent t variables. We show that such variable order of differentiation can be approached with the theory of fractional integration and the associate variable order ordinary differential equations (VODE) can be solved as Volterra integral equations of second kind with singular integrable kernel. We find the conditions for existence and uniqueness of solutions of such VODE, and present some numeric solutions for particular cases exhibiting bifurcations and blow-up.