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In this paper, the fractional projective Riccati expansion method is proposedto solve fractional differential equations. To illustrate the effectiveness ofthe method, we discuss the space-time fractional Burgers equation, thespace-time fractional mKdV equation and time fractional biological populationmodel. The solutions are expressed in terms of fractional hyperbolic functions.These solutions are useful to understand the mechanisms of the complicatednonlinear physical phenomena and fractional differential equations. Among thesesolutions, some are found for the first time. The fractal index for theobtained results is equal to one. Counter examples to compute the fractal indexare introduced in appendix.

Solution of nonlinear space time fractional differential equations via the fractional projective Riccati expansion method