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SOME ANALYTICAL SOLUTIONS BY MAPPING METHODS FOR NON-LINEAR CONFORMABLE TIME-FRACTIONAL PHI-4 EQUATION

ABSTRACT
In this paper, the practice of two types of mapping methods are used to solve the time fractional Phi-four equation by means of conformable fractional derivative. The solutions are derived using Jacobi's elliptic functions for two different value of the modulus and are obtained the some soliton solutions. The found solutions are identified bright optical soliton, dark soliton, singular soliton, combo soliton solution and periodic solutions.
KEYWORDS
PAPER SUBMITTED: 2019-01-08
PAPER REVISED: 2019-06-20
PAPER ACCEPTED: 2019-07-10
PUBLISHED ONLINE: 2019-09-15
DOI REFERENCE: https://doi.org/10.2298/TSCI190108341K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 6, PAGES [S1815 - S1822]
REFERENCES
  1. Mohyud-Din, S.T., Travelling wave solutions of seventh-order generalized KdV equations using He's polynomials, International Journal of Nonlinear Sciences and Numerical Simulation 10(2), 223-229, 2009.
  2. Mohyud-Din, S.T., et al., Numerical soliton solution of the Kaup-Kupershmidt equation, International Journal of Numerical Methods for Heat & Fluid Flow 21(3), (2011), 272-281.
  3. Khan,U., et al., Extracting new solitary wave solutions of Benny-Luke equation and Phi-4 equation of fractional order by using (G'/G)-expansion method, Opt Quant Electron (2017) 49:362.
  4. Sikander, W., et al., Optimal solutions for homogeneous and non-homogeneous equations arising in physics, Results in Physics 7 (2017) 216-224.
  5. Sikander, W., et al., Optimal solutions for the evolution of a social obesity epidemic model, Eur. Phys. J. Plus (2017) 132: 257.
  6. Mohyud-Din, S.T., et al., Exact solutions of (3 + 1)-dimensional generalized KP equation arising inphysics, Results in Physics 7 (2017) 3901-3909.
  7. Mirzazadeh, M., et al., Soliton solutions of the generalized Klein-Gordon equation by using G'/G -expansion method, Computational and Applied Mathematics 33 (3), (2014)831-839.
  8. Mirzazadeh, M., et al., Solitons and other solutions to Wu-Zhang system, Nonlinear Analysis: Modelling and Control, (2017), 22,4, 441-458.
  9. Mirzazadeh, M., et al., Exact solutions of the Kudryashov-Sinelshchikov equation and nonlinear telegraph equation via the first integral method, Nonlinear Anal. Model 17 (4), (2012)481-488.
  10. Eslami.,M., Trial solution technique to chiral nonlinear Schrodinger''s equation in (1+2)-dimensions, Nonlinear Dynamics 85 (2),(2016) 813-816.
  11. Zhou Q., et al., Optical solitons with Biswas-Milovic equation by extended trial equation method, Nonlinear Dynamics 84 (4),(2016) 1883-1900.
  12. Eslami.,M., et al., First integral method to look for exact solutions of a variety of Boussinesq-like equations, Ocean Engineering 83,(2014) 133-137.
  13. Ekici, M., et al., Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives, Optik, 127 (2016), pp. 10659-10669.
  14. Tchier, F., et al., Solution of the time fractional reaction-diffusion equations with residual power series method, Advances in Mechanical Engineering, 8(10) (2016),pp. 1-10.
  15. Rezazadeh, H., et al., Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method, Optical and Quantum Electronics 50 (3)(2018), 150.
  16. Inc, M., et al., A new method for approximate solution of some nonlinear equations: Residual power series method, Advances in Mechanical Engineering, 8(4) (2016), pp. 1-7.
  17. Eslami,M., Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Applied Mathematics and Computation (2016)285, 141-148.
  18. Korpinar, Z., On numerical solutions for the Caputo-Fabrizio fractional heat-like equation, Thermal Science, 22(1) (2018), pp. 87-95.
  19. Rezazadeh, H., et al., New exact solutions of nonlinear conformable time-fractional Phi-4 equation, Chinese Journal of Physics 56 (2018), pp. 2805-2816.
  20. Deng, X., et al., Travelling wave solutions for a nonlinear variant of the PHI-four equation, Math. Comp. Model. 49 (3-4) (2009), pp. 617-622.
  21. Akter, J., and Akbar, M.A., Exact solutions to the Benney-Luke equation and the Phi-4 equations by using modified simple equation method, Results Phys. 5 (2015), pp. 125-130.
  22. Bhrawy, A.H., et al., An efficient spectral collocation algorithm for nonlinear Phi-four equations, Bound. value probl. (1) (2013), pp. 87
  23. Triki, H., and Wazwaz, A.M., Envelope solitons for generalized forms of the phi-four equation, J. King Saud Univ., 25 (2) (2013), pp. 129-133.
  24. Tariq, H., and Akram, G., New approach for exact solutions of time fractional Cahn-Allen equation and time fractional Phi-4 equation, Phys. A, 473 (2017), pp. 352-362.
  25. Alquran, M., et al., Analytical solution of the time-fractional Phi-4 equation by using modified residual power series method, Nonlinear Dyn, 90 (4) (2017), pp. 2525-2529.
  26. Krishnan, E.V., Mapping methods to solve a modified Korteweg-de Vries equation, SQU J. Sci. 20 (2) (2015), pp. 42-48.
  27. Krishnan, E.V., Biswas, A., Solutions to the Zakharov--Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods, Phys. Wave Phenom. 18 (2010), pp. 256-261.
  28. Krishnan, E.V., et al., Solitons in optical metamaterials by mapping method, J.Optoelectron. Adv. Mater. 17 (3-4) (2015), pp. 511-516.
  29. Peng, Y., Exact periodic wave solutions to a new Hamiltonian amplitude equation, J. Phys. Soc. Jpn. 72 (6) (2003), pp. 1356-1359.
  30. Krishnan, E.V., et al., Optik - International Journal for Light and Electron Optics 178 (2019), pp. 104-110.
  31. Peng, Y., New exact solutions to a new Hamiltonian amplitude equation II, J. Phys. Soc. Jpn., 73 (5) (2004), pp. 1156-1158.
  32. Khalil, R., et al., A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), pp. 65-70.
  33. Eslami, M., and Rezazadeh, H., The first integral method for Wu-Zhang system with conformable time-fractional derivative, Calcolo 53 (3) (2016), pp. 475-485.
  34. Çenesiz, Y., et al., New exact solutions of Burgers' type equations with conformable derivative, Waves Random Complex Media, 27 (1) (2017), pp. 103-116.
  35. Eslami, M., et al., The first integral method applied to the Bogoyavlenskii equations by means of conformable fractional derivative, Opt. Quant. Electron. 49 (12) (2017), pp. 391.
  36. Rezazadeh, H., et al., Mitigating internet bottleneck with fractional temporal evolution of optical solitons having quadratic-cubic nonlinearity, Optik. 164 (2018), pp. 84-92.
  37. Rezazadeh, H., et al., Traveling wave solutions for density-dependent conformable fractional diffusion-reaction equation by the rst integral method and the improved tan(3c6(3be)/2)-expansion method, Opt. Quant. Electron. 50 (3) (2018), pp. 12.
  38. Hosseini, K., et al., Bright and singular soliton solutions of the conformable time-fractional Klein-Gordon equations with different nonlinearities, Waves Random Complex Media 28 (3) (2018), pp. 426-434.

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