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Observations of fractional effects of β-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques

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  • Akram, Ghazala
  • Sadaf, Maasoomah
  • Zainab, Iqra

Abstract

The presented work deals with the investigation of space time fractional Phi-4 model which has great importance in particle and nuclear physics. Two eminent techniques, namely, the extended (G′G2)-expansion method and the modified auxiliary equation (MAE) method are utilized to construct the traveling wave solutions of fractional Phi-4 model. The fractional effects on the model are studied using the β-derivative and M-truncated derivative. The obtained results include trigonometric and hyperbolic functions with dark and periodic traveling wave behaviors. Comparison of fractional effects for the β-derivative and M-truncated derivative is illustrated through graphs by assigning particular values to fractional parameter. The obtained results will be helpful to understand the dynamical framework of time fractional Phi-4 model in the related physical phenomena.

Suggested Citation

  • Akram, Ghazala & Sadaf, Maasoomah & Zainab, Iqra, 2022. "Observations of fractional effects of β-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009991
    DOI: 10.1016/j.chaos.2021.111645
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    References listed on IDEAS

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    1. Sekson Sirisubtawee & Sanoe Koonprasert, 2018. "Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the -Expansion Method," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-15, June.
    2. Salahshour, S. & Ahmadian, A. & Abbasbandy, S. & Baleanu, D., 2018. "M-fractional derivative under interval uncertainty: Theory, properties and applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 84-93.
    3. Kilic, Bulent & Inc, Mustafa, 2015. "The First Integral Method for the time fractional Kaup-Boussinesq System with time dependent coefficient," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 70-74.
    4. Inc, Mustafa, 2007. "New compacton and solitary pattern solutions of the nonlinear modified dispersive Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1275-1284.
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    Cited by:

    1. Zainab, Iqra & Akram, Ghazala, 2023. "Effect of β-derivative on time fractional Jaulent–Miodek system under modified auxiliary equation method and exp(−g(Ω))-expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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