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Journals / NATURENGS / 2020 / Cilt: 1 - Sayı: 1

New analytical solutions for space and time fractional Phi-4 equation

Ayşegül DAŞCIOĞLU
Sevil ÇULHA ÜNAL
Dilek VAROL BAYRAM
Journal
NATURENGS
Pages
30–46
Publication Date
2020-06-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Four problems are presented to illustrate the application of the method and some of the solutions are also demonstrated by the graphics.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, by utilizing an analytical method based on the Jacobi elliptic functions, the largest set in the literature of time, space and space-time conformable fractional Phi-4 equations is found.
📊
Key Findings & Data:These solutions are obtained in general form including rational, trigonometric, hyperbolic and complex functions.
💡
Conclusion & Impact:Four problems are presented to illustrate the application of the method and some of the solutions are also demonstrated by the graphics.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Jacobi elliptic functions · Space-time fractional Phi-4 equation · Conformable fractional derivative

Abstract

In this paper, by utilizing an analytical method based on the Jacobi elliptic functions, the largest set in the literature of time, space and space-time conformable fractional Phi-4 equations is found. These solutions are obtained in general form including rational, trigonometric, hyperbolic and complex functions. Four problems are presented to illustrate the application of the method and some of the solutions are also demonstrated by the graphics.

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Cite This Article

DAŞCIOĞLU, A., ÜNAL, S. Ç., BAYRAM, D. V. (2020). New analytical solutions for space and time fractional Phi-4 equation. NATURENGS, Cilt: 1 - Sayı: 1, 30–46. https://ajindex.com/articles/793337

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References (15)

  1. Lundquist, S., March, N. H. and Tosi, M. P., (1988), Order and Chaos in Nonlinear Physical systems, Springer, New York
  2. Calogero, F. and Degasperis, A., (1982), Spectral Transform and Solitons: Tools to solve and Investigate Nonlinear Evolution Equations, New York: North-Holland
  3. Wazwaz, A. M., (2007), Analytic study on nonlinear variants of the RLW and the PHI-four equations, Communications in Nonlinear Science and Numerical Simulation 12, 314–327
  4. Wazwaz, A. M., (2005), Generalized forms of the phi-four equation with compactons, solitons and periodic solutions, Mathematics and Computers in Simulation, 69, 580–588
  5. Alofi, A. S., (2013), Exact and Explicit Traveling Wave Solutions for the Nonlinear Partial Differntial Equations, World Applied Sciences Journal, 21, 62-67
  6. Soliman, A. A., (2007), Exact travelling wave solution of nonlinear variants of the RLW and the PHI-four equations, Physics Letters A, 368, 383–390
  7. Deng, X., Zhao, M. and Li, X., (2009), Travelling wave solutions for a nonlinear variant of the PHI-four equation, Mathematical and Computer Modelling, 49, 617–622
  8. Xiang, C., (2012), A note on exact travelling wave solutions for nonlinear PHI-four equation, Applied Mechanics and Materials, 4569-4572
  9. Najafi, M., (2012), Using He’s Variational Method to Seek the Traveling Wave Solution of PHI-Four Equation, International Journal of Applied Mathematical Research, 1 (4), 659-665
  10. Younis, M. and Zafar, A., (2013), The modified simple equation method for solving nonlinear Phi-Four equation, International Journal of Innovation and Applied Studies, 2, 661-664
  11. Akter, J. and Akbar, M. A., (2015), Exact solutions to the Benney–Luke equation and the Phi-4 equations by using modified simple equation method, Results in Physics, 5, 125-130
  12. Ehsani, F., Ehsani, F., Hadi, A. and Hadi, A., (2013), Analytical Solution of Phi-Four Equation, Technical Journal of Engineering and Applied Sciences, 3 (14), 1378-1388
  13. Akbulut, A., Kaplan, M. and Tascan, F., (2016), Conservation laws and Exact Solutions of Phi-Four (Phi-4) Equation via the (G^'⁄G,1⁄G )- Expansion Method, Naturforsch, 71 (5), 439-446
  14. Zahra, W. K., (2017), Trigonometric B-Spline Collocation Method for Solving PHI-Four and Allen–Cahn Equations, Mediterranean Journal of Mathematics, 14, 122-141
  15. Mahmud, F., Samsuzzoha, M. and Akbar, M. A., (2017), A generalized Kudrashov method to obtain exact travelling wave solutions of the PHI-four eq