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Lie symmetry analysis, explicit solutions and conservation laws for the space–time fractional nonlinear evolution equations

Author

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

Abstract

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space–time fractional nonlinear evolution equations with Riemann–Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi–Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:496:y:2018:i:c:p:371-383
    DOI: 10.1016/j.physa.2017.12.119
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    References listed on IDEAS

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    1. 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.
    2. Ali, Khalid K. & Nuruddeen, R.I. & Raslan, K.R., 2018. "New structures for the space-time fractional simplified MCH and SRLW equations," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 304-309.
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    Cited by:

    1. Aljohani, A.F. & Hussain, Q. & Zaman, F.D. & Kara, A.H., 2021. "On a study of some classes of the fourth-order KdV–Klein/Gordon equation and its time fractional forms," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Zhang, Yi, 2019. "Lie symmetry and invariants for a generalized Birkhoffian system on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 306-312.
    3. Aljohani, A.F. & Alqurashi, Bader Mutair & Kara, A.H., 2021. "Solitons, travelling waves, invariance, conservation laws and ‘approximate’ conservation of the extended Jimbo-Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. 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.
    5. Fan Qin & Wei Feng & Songlin Zhao, 2022. "Lie Symmetry Group, Invariant Subspace, and Conservation Law for the Time-Fractional Derivative Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    6. 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.
    7. 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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