  A method for the numerical solution of variable order (VO) fractional
differential equations (FDE) is presented. The method applies to linear as well
as to nonlinear VO-FDEs. The Caputo type VO fractional derivative is employed.
First, an simple expression, which approximates the VO fractional derivative,
is established and then a procedure based on this approximation is developed to
solve VO-FDEs linear and nonlinear, both explicit and implicit. VO-FDEs with
variable coefficients are also treated. The method is illustrated by solving
the second order VO-FDE describing the response of the VO fractional
oscillator, linear and nonlinear (Duffing). However, it can be
straightforwardly extended to higher order VO-FDEs. The presented method, in
addition to its effectiveness, is simple to implement and program on a
computer. The obtained results validate the efficiency and accuracy of the
developed method
