New exact solutions of nonlinear conformable time-fractional Phi-4 equation

Tariq, 2016, New traveling wave exact and approximate solutions for the nonlinear Cahn-Allen equation: evolution of a nonconserved quantity, Nonlinear Dy, 88, 581, 10.1007/s11071-016-3262-7

J.Ablowitz, 1991, Vol. 149

Schamel, 1973, A modified Korteweg-de Vries equation for ion acoustic wavess due to resonant electrons, J. Plasma Phys., 9, 377, 10.1017/S002237780000756X

Kadomtsev, 1970, On the stability of solitary waves in weakly dispersing media, Sov. Phys. Dokl., 15, 539

Kadomtsev, 1978, Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Sov. Phys. JETP., 74, 1017

Hosseini, 2018, New optical solitons of cubic-quartic nonlinear Schrödinger equation, Optik, 157, 1101, 10.1016/j.ijleo.2017.11.124

Hosseini, 2017, New exact traveling wave solutions of the unstable nonlinear Schrödinger equations, Commun. Theor. Phys., 68, 761, 10.1088/0253-6102/68/6/761

Hosseini, 2017, New exact traveling wave solutions of the Tzitzéica-type evolution equations arising in non-linear optics, J. Modern Opt., 64, 1688, 10.1080/09500340.2017.1302607

Ayati, 2017, Application of Kudryashov and functional variable methods to the strain wave equation in microstructured solids, Nonlinear Eng., 6, 25, 10.1515/nleng-2016-0020

Hosseini, 2018, New explicit exact solutions of the unstable nonlinear Schrödinger's equation using the expa and hyperbolic function methods, Opt. Quant. Electron., 50, 82, 10.1007/s11082-018-1350-2

Kumar, 2018, Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chin. J. Phys., 56, 75, 10.1016/j.cjph.2017.11.020

Sarwar, 2018, Stability analysis, dynamical behavior and analytical solutions of nonlinear fractional differential system arising in chemical reaction, Chin. J. Phys., 56, 374, 10.1016/j.cjph.2017.11.009

Sun, 2015, Bright soliton solutions of the coherently-coupled nonlinear Schrödinger equations in optical fibers, Chin. J. Phys., 53, 1

Cheng, 2007, Exact solutions of the Klein-Gordon equation with a ring-shaped modified Kratzer potential, Chin. J. Phys., 45, 480

Ghany, 2015, Exact travelling wave solutions for stochastic fractional Hirota-Satsuma coupled KdV equations, Chin. J. Phys., 53, 153

Khader, 2014, An accurate numerical method for solving the linear fractional Klein-Gordon equation, Math. Methods Appl. Sci., 37, 2972, 10.1002/mma.3035

Ebaid, 2009, solutions for the generalized Klein-Gordon equation via a transformation and Exp-function method and comparison with Adomian's method, J. Comput. Appl. Math., 223, 278, 10.1016/j.cam.2008.01.010

Dashen, 1975, Particle spectrum in model field theories from semiclassical functional integral techniques, Phys. Rev. D, 11, 3424, 10.1103/PhysRevD.11.3424

Deng, 2009, Travelling wave solutions for a nonlinear variant of the PHI-four equation, Math. Comp. Model., 49, 617, 10.1016/j.mcm.2008.03.011

Akter, 2015, Exact solutions to the Benney-Luke equation and the Phi-4 equations by using modified simple equation method, Results Phys., 5, 125, 10.1016/j.rinp.2015.01.008

Bhrawy, 2013, An efficient spectral collocation algorithm for nonlinear Phi-four equations, Bound. value probl., 87, 10.1186/1687-2770-2013-87

Triki, 2013, Envelope solitons for generalized forms of the phi-four equation, J. King Saud Univ., 25, 129, 10.1016/j.jksus.2012.08.001

Tariq, 2017, New approach for exact solutions of time fractional Cahn-Allen equation and time fractional Phi-4 equation, Phys. A, 473, 352, 10.1016/j.physa.2016.12.081

Alquran, 2017, Analytical solution of the time-fractional Phi-4 equation by using modified residual power series method, Nonlinear Dyn, 90, 2525, 10.1007/s11071-017-3820-7

Khalil, 2014, A new definition of fractional derivative, J. Comput. Appl. Math., 264, 65, 10.1016/j.cam.2014.01.002

Eslami, 2016, The first integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo, 53, 475, 10.1007/s10092-015-0158-8

Çenesiz, 2017, New exact solutions of Burgers’ type equations with conformable derivative, Waves Random Complex Media, 27, 103, 10.1080/17455030.2016.1205237

Eslami, 2017, The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative, Opt. Quant. Electron., 49, 391, 10.1007/s11082-017-1224-z

Khodadad, 2017, Solutions of the conformable fractional Zakharov-Kuznetsov equation with dual-power law nonlinearity, Opt. Quant. Electron., 49, 384, 10.1007/s11082-017-1225-y

Korkmaz, 2017, Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods, Opt. Quant. Electron., 49, 278, 10.1007/s11082-017-1116-2

Eslami, 2017, Exact solutions to the space-time fractional Schr¨odinger-Hirota equation and the space-time modied KDV-ZakharovKuznetsov equation, Opt.Quant. Electron., 49, 279, 10.1007/s11082-017-1112-6

Rezazadeh, 2018, Mitigating internet bottleneck with fractional temporal evolution of optical solitons having quadratic-cubic nonlinearity, Optik., 164, 84, 10.1016/j.ijleo.2018.03.006

Rezazadeh, 2018, Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method, Opt. Quant. Electron., 50, 150, 10.1007/s11082-018-1416-1

Aminikhah, 2016, Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives, Sci. Iran., 23, 1048

Rezazadeh, 2018, Traveling wave solutions for density-dependent conformable fractional diffusion-reaction equation by the rst integral method and the improved tan(φ(ξ)/2)-expansion method, Opt. Quant. Electron., 50, 12

Hosseini, 2018, Bright and singular soliton solutions of the conformable time-fractional Klein-Gordon equations with different nonlinearities, Waves Random Complex Media, 28, 426, 10.1080/17455030.2017.1362133

Hosseini, 2017, Resonant optical solitons with perturbation terms and fractional temporal evolution using improved tan(ϕ(η)/2)-expansion method and exp function approach, Optik, 158, 933, 10.1016/j.ijleo.2017.12.139

Hosseini, 2017, Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the exp(-ϕ)-expansion method, Opt. Quant. Electron., 49, 131, 10.1007/s11082-017-0968-9

Younis, 2015, Dispersive dark optical soliton in (2+1)-dimensions by (G′/G)-expansion with dual-power law nonlinearity, Optik, 126, 5812, 10.1016/j.ijleo.2015.08.233

Ryabov, 2011, Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations, Appl. Math. Comput., 218, 3965

Hosseini, 2017, Modified Kudryashov method for solving the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities, Optik, 130, 737, 10.1016/j.ijleo.2016.10.136

Neirameh, 2015, New exact solitary wave solutions to the TDB and (2+1)-DZ equations, Palest. J. Math., 4, 386

Zheng, 2002, New exact traveling wave solutions for compound KdV-Burgers equations in mathematical physics, Appl. Math. E-Notes., 2, 45

Wazwaz, 2007, The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations, Appl. Math. Comput., 184, 1002

Rezazadeh, 2018, New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity, Optik, 167, 218, 10.1016/j.ijleo.2018.04.026

Bashir, 2014, The coth_a(ξ) expansion method and its application to the Davey-Stewartson equation, Appl. Math. Comput., 8, 3851