  In this paper, the fractional projective Riccati expansion method is proposed
to solve fractional differential equations. To illustrate the effectiveness of
the method, we discuss the space-time fractional Burgers equation, the
space-time fractional mKdV equation and time fractional biological population
model. The solutions are expressed in terms of fractional hyperbolic functions.
These solutions are useful to understand the mechanisms of the complicated
nonlinear physical phenomena and fractional differential equations. Among these
solutions, some are found for the first time. The fractal index for the
obtained results is equal to one. Counter examples to compute the fractal index
are introduced in appendix.
