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Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis

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  • Inc, Mustafa
  • Yusuf, Abdullahi
  • Isa Aliyu, Aliyu
  • Baleanu, Dumitru

Abstract

This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn–Allen (CA) and time-fractional Klein–Gordon (KG) equations with Riemann–Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented.

Suggested Citation

  • Inc, Mustafa & Yusuf, Abdullahi & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Time-fractional Cahn–Allen and time-fractional Klein–Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 94-106.
    • Handle: RePEc:eee:phsmap:v:493:y:2018:i:c:p:94-106
    DOI: 10.1016/j.physa.2017.10.010
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    References listed on IDEAS

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    1. Huang, Qing & Zhdanov, Renat, 2014. "Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 110-118.
    2. Hashemi, M.S., 2015. "Group analysis and exact solutions of the time fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 141-149.
    3. Tariq, Hira & Akram, Ghazala, 2017. "New approach for exact solutions of time fractional Cahn–Allen equation and time fractional Phi-4 equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 352-362.
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    Cited by:

    1. Mohammadizadeh, Fatemeh & Rashidi, Saeede & Hejazi, S. Reza, 2021. "Space–time fractional Klein-Gordon equation: Symmetry analysis, conservation laws and numerical approximations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 476-497.
    2. Berhe, Hailay Weldegiorgis & Qureshi, Sania & Shaikh, Asif Ali, 2020. "Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Stanislav Yu. Lukashchuk, 2022. "On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    4. Zhang, Zhi-Yong & Li, Guo-Fang, 2020. "Lie symmetry analysis and exact solutions of the time-fractional biological population model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Jeong, Darae & Li, Yibao & Choi, Yongho & Lee, Chaeyoung & Yang, Junxiang & Kim, Junseok, 2021. "A practical adaptive grid method for the Allen–Cahn equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    6. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 520-531.
    7. Hashemizadeh, E. & Ebrahimzadeh, A., 2018. "An efficient numerical scheme to solve fractional diffusion-wave and fractional Klein–Gordon equations in fluid mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1189-1203.
    8. Inc, Mustafa & Yusuf, Abdullahi & Aliyu, Aliyu Isa & Baleanu, Dumitru, 2018. "Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 371-383.
    9. Khalique, Chaudry Masood & Motsepa, Tanki, 2018. "Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 871-879.
    10. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.

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