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The objective of this article is to construct new and further general analytical wave solutions to some nonlinear evolution equations of fractional order in the sense of the modified Riemann-Liouville derivative relating to mathematical physics, namely, the space-time fractional Fokas equation, the time fractional nonlinear model equation and the space-time fractional (2 + 1)-dimensional breaking soliton equation by exerting a rather new mechanism (G'/G,1/G) -expansion method. We use the fractional complex transformation and associate the fractional differential equations to the solvable integer order differential equations. A comprehensive class of new and broad-ranging exact traveling and solitary wave solutions are revealed in terms of trigonometric, rational and hyperbolic functions. The attained wave solutions are sketched graphically by using Mathematica and make a comparison to the results attained by the presented technique with other techniques in a comprehensive manner. It is notable that the method can be considered as a reduction of the reputed (G'/G) -expansion method commenced by Wang et al. It is noticeable that, the two variable (G'/G,1/G) -expansion method appears to be more reliable, straightforward, computerized and user-friendly.