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The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation

Author

Listed:
  • Hasan Bulut
  • Haci Mehmet Baskonus
  • Yusuf Pandir

Abstract

The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give to us approximate solutions; others give to us analytical solutions. In this paper, we applied the modified trial equation method (MTEM) to the one-dimensional nonlinear fractional wave equation (FWE) and time fractional generalized Burgers equation. Then, we submitted 3D graphics for different value of .

Suggested Citation

  • Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    • Handle: RePEc:hin:jnlaaa:636802
    DOI: 10.1155/2013/636802
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    Cited by:

    1. B. A. Jacobs & C. Harley, 2014. "Two Hybrid Methods for Solving Two‐Dimensional Linear Time‐Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Liu, Cheng-shi, 2018. "Counterexamples on Jumarie’s three basic fractional calculus formulae for non-differentiable continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 219-222.
    3. Zeshan Aslam Khan & Naveed Ishtiaq Chaudhary & Syed Zubair, 2019. "Fractional stochastic gradient descent for recommender systems," Electronic Markets, Springer;IIM University of St. Gallen, vol. 29(2), pages 275-285, June.
    4. Kai, Yue & Li, Yaxi & Huang, Liuke, 2022. "Topological properties and wave structures of Gilson–Pickering equation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Kai Fan & Cunlong Zhou, 2020. "Mechanical Solving a Few Fractional Partial Differential Equations and Discussing the Effects of the Fractional Order," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    6. M. Al-Amin & M. Nurul Islam & Onur Alp İlhan & M. Ali Akbar & Danyal Soybaş, 2022. "Solitary Wave Solutions to the Modified Zakharov–Kuznetsov and the (2 + 1)‐Dimensional Calogero–Bogoyavlenskii–Schiff Models in Mathematical Physics," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    7. Seyma Tuluce Demiray & Yusuf Pandir & Hasan Bulut, 2014. "Generalized Kudryashov Method for Time‐Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Özkan Güner & Dursun Eser, 2014. "Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    9. Dianchen Lu & Chen Yue & Muhammad Arshad, 2017. "Traveling Wave Solutions of Space‐Time Fractional Generalized Fifth‐Order KdV Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).

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