Communicated by I. StratisIn this study, the nonlinear fractional partial differential equations have been defined by the modified Riemann-Liouville fractional derivative. By using this fractional derivative and traveling wave transformation, the nonlinear fractional partial differential equations have been converted into nonlinear ordinary differential equations. The modified trial equation method is implemented to obtain exact solutions of the nonlinear fractional Klein-Gordon equation and fractional clannish random walker's parabolic equation. As a result, some exact solutions including single kink solution and periodic and rational function solutions of these equations have been successfully obtained.

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In this paper, exact analytical solutions of the biological population model, the EW and the modified EW equations with a conformable derivative operator have been examined by means of the trial solution algorithm and the complete discrimination system. Dark, bright and singular traveling wave solutions of the equations have been obtained by algorithm. Also, revealed singular periodic solutions have been listed. All solutions were verified by substituting them into their corresponding equation via Mathematica package program.

In this work, we investigate exact solutions of some fractional‐order differential equations arising in mathematical physics. We consider the space‐time fractional Kaup‐Kupershmidt, the space‐time fractional Fokas, and the space‐time fractional breaking soliton equations, which have important applications in science and engineering. Exact traveling wave solutions of these equations have been established by different efficient methods.