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In this paper, we firstly give a counterexample to indicate that the chain rule is lack of accuracy. After that, we put forward the fractional Riccati expansion method. No need to use the chain rule, we apply this method to fractional KdV-type and fractional Telegraph equations and obtain the tangent and cotangent functions solutions of these fractional equations for the first time.

The Traveling Wave Solutions of Space-Time Fractional Differential Equation Using Fractional Riccati Expansion Method