( $$\frac{G^{'}}{G^{2}}$$ G ′ G 2 )-Expansion method: new traveling wave solutions for some nonlinear fractional partial differential equations

Abdoon, M.A.: First integral method: a general formula for nonlinear fractional Klein–Gordon equation using advanced computing language. Am. J. Comput. Math. 5, 127–134 (2015)

Aksoy, E., Kaplan, M., Bekir, A.: Exponential rational function method for space-time fractional differential equations. Waves Random Complex Med. 26(2), 142–151 (2016)

Alzaidy, J.F.: The fractional sub-equation method and exact analytical solutions for some nonlinear fractional PDEs. Am. J. Math. Anal. 1(1), 14–19 (2013)

Bekir, A., Güner, Ö.: Exact solutions of nonlinear fractional differential equations by $$\frac{G^{{\prime }}}{G}$$ G ′ G -expansion method. Chin. Phys. B 22(11), 110202 (2013)

Bekir, A., Güner, Ö., Cevikel, A.C.: Fractional complex transform and exp-function methods for fractional differential equations. Abstr. Appl. Anal. 426462, 8 (2013)

Bekir, A., Güner, Ö., Aksoy, E., Pandir, Y.: Functional variable method for the nonlinear fractional differential equations. AIP Conf. Proc. 1648, 730001 (2015)

Bekir, A., Guner, O., Cevikel, A.: The exp-function method for some time-fractional differential equations. J. Autom. Sinica 4(2), 315–321 (2017)

Bulut, H., Pandir, Y.: Modified trial equation method to the nonlinear fractional Sharma–TassoOlever equation. Int. J. Model. Optim. 3(4), 353–357 (2013)

Bulut, H., Baskonus, H.M., Pandir, Y.: The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. Abstr. Appl. Anal. 636802, 8 (2013)

Chen, J., Chen, H.: The ( $$\frac{G^{{\prime }}}{G^{2}}$$ G ′ G 2 )- -expansion method and its application to coupled nonlinear Klein–Gordon Equation. J. South China Normal Univ. (Natural Sci. Ed.) 2, 13 (2012)

Çenesiz, Y., Tasbozanand, O., Kurt, A.: Functional variable method for conformable fractional modified KdV–ZK equation and Maccari system. Tbilisi Math. J. 10(1), 117–125 (2017)

Diethelm, K., Ford, N.J.: Analysis of fractional differential equations. J. Math. Anal. Appl. 265, 229–248 (2002)

Ege, S.M., Misirli, E.: The modified Kudryashov method for solving some fractional-order nonlinear equations. Adv. Differ. Equ. 135, 1–13 (2014)

Güner, O., Bekir, A., Cevikel, A.C.: A variety of exact solutions for the time fractional Cahn–Allen equation. Eur. Phys. J. Plus 130(146), 1–13 (2015)

Güner, Ö., Cevikel, A.C.: A procedure to construct exact solutions of nonlinear fractional differential equations. Sci. World J. 2014, 489495 (2014)

Hosseini, K., Ansari, R.: New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method. Waves Random Complex Med. 2017, 1–9 (2017)

Hosseinia, K., Bekir, A., Ansari, R.: New exact solutions of the conformable time-fractional Cahn–Allen and Cahn–Hilliard equations using the modified Kudryashov method. Optik: Int. J. Light Electron. Opt. 132, 203–209 (2017)

Inc, M.: The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method. J. Math. Anal. Appl. 345, 476–484 (2008)

Jafari, H., Tajadodi, H., Kadkhoda, N., Baleanu, D.: Fractional sub-equation method for Cahn–Hilliard and Klein–Gordon equations. Abstr. Appl. Anal. 587179, 5 (2013)

Kaplan, M., Koparan, M., Bekir, A.: Regarding on the exact solutions for the nonlinear fractional differential equations. Open Phys. 14, 478–482 (2016)

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)

Liu, W., Chen, K.: The functional variable method for finding exact solutions of some nonlinear time-fractional differential equations. Pramana 81(3), 377–384 (2013)

Lu, B.: The first integral method for some time fractional differential equations. J. Math. Anal. Appl. 395, 684–693 (2012)

Machado, J.T., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear. Sci. Numer. Simul. 16, 1140–1153 (2011)

Matinfar, M., Eslami, M., Kordy, M.: The functional variable method for solving the fractional Kortewegde Vries equations and the coupled Kortewegde Vries equations. Indian Acad. Sci. 85(4), 583592 (2015)

Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, Hoboken (1993)

Mohyud-Din, S.T., Nawaz, T., Azhar, E., Akbar, M.A.: Fractional sub-equation method to space-time fractional Calogero–Degasperis and potential Kadomtsev–Petviashvili equations. J. Taibah Univ. Sci. 11, 258–263 (2017)

Mohyud-Din, S.T., Bibi, S.: Exact solutions for nonlinear fractional differential equations using $$\frac{G^{{\prime }}}{G}$$ G ′ G -expansion method. Alex. Eng. J. https://doi.org/10.1016/j.aej.2017.01.035 (2017)

Mohyud-Din, S.T., Bibi, S.: Exact solutions for nonlinear fractional differential equations using $$\frac{G^{{\prime }}}{G^{2}}$$ G ′ G 2 -expansion method. Alex. Eng. J. (2017)

Podlubny, I.: Fractional Differential Equations. Academic Press, California (1999)

Raslan, K.R.: The first integral method for solving some important nonlinear partial differential equations. Nonlinear Dyn. 53(4), 281–286 (2008)

Sahoo, S., Ray, S.S.: Improved fractional sub-equation method for (3+1)-dimensional generalized fractional KdV-Zakharov–Kuznetsov equations. Comput. Math. Appl. 70(2), 158–166 (2015)

Shang, N., Zheng, B.: Exact solutions for three fractional partial differential equations by the $$\frac{G^{{\prime }}}{G}$$ G ′ G method. IAENG Int. J. Appl. Math. 43(3), 1–6 (2013)

Wang, G., Xu, T.Z.: The modified fractional sub-eqution method and its applications to nonlinear fractional partial differential equations. Roman. J. Phys. 59, 636–645 (2014)

Yan, L.-M., Xu, F.-S.: Generalizied Exp-function method for nonlinear space time fractional differential equations. Therm. Sci. 18(5), 1573–1576 (2014)

Younis, M.: A new approach for the exact solutions of nonlinear equations of fractional order via modified simple equation method. Appl. Math. 5, 1927–1932 (2014)

Younis, M., Zafar, A.: Exact solution to nonlinear differential equations of fractional order via $$\frac{G^{{\prime }}}{G}$$ G ′ G -expansion method. Appl. Math. 5, 1–6 (2014)

Ypez-Martnez, H., Sosa, I.O., Reyes, J.M.: Fengs first integral method applied to the ZKBBM and the generalized fisher space-time fractional equations. J Appl Math 191545, 9 (2015)

Zayed, E.M.E., Amer, Y.A., Al-Nowehy, A.-G.: The modified simple equation method and the multiple exp-function method for solving nonlinear fractional Sharma-Tasso-Olver Equation. Acta Mathematicae Applicatae Sinica 32(4), 793–812 (2016)

Zayed, E.M.E., Hoda Ibrahim, S.A.: Modified simple equation method and its applicationsfor some nonlinear evolution equations in mathematical physics. Int. J. Comput. Appl. 67(6), 39–44 (2013)

Zhang, S., Zhang, H.-Q.: Fractional sub-equation method and its applications to nonlinear fractional PDEs. Phys. Lett. A 375(7), 1069–1073 (2011)

Zheng, B.: Exp-function method for solving fractional partial differential equations. Sci. World J. 465723, 8 (2013)