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Time fractional third-order variant Boussinesq system: Symmetry analysis, explicit solutions, conservation laws and numerical approximations

  • Fairouz Tchier
  • Mustafa IncEmail author
  • Abdullahi Yusuf
  • Aliyu Isa Aliyu
  • Dumitru Baleanu
Regular Article
  • 116 Downloads

Abstract.

The current work provides comprehensive investigation for the time fractional third-order variant Boussinesq system (TFTOBS) with Riemann-Liouville (RL) derivative. Firstly, we obtain point symmetries, similarity variables, similarity transformation and reduce the governing equation to a special system of ordinary differential equation (ODE) of fractional order. The reduced equation is in the Erdelyi-Kober (EK) sense. Secondly, we solve the reduced system of ODE using the power series (PS) expansion method. The convergence analysis for the power series solution is analyzed and investigated. Thirdly, the new conservation theorem and the generalization of the Noether operators are applied to construct nonlocal conservation laws (CLs) for the TFTOBS. Finally, we use residual power series (RPS) to extract numerical approximation for the governing equations. Interesting figures that explain the physical understanding for both the explicit and approximate solutions are also presented.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.King Saud UniversityDepartment of Applied MathematicsRiyadhSaudi Arabia
  2. 2.Firat UniversityScience Faculty, Department of MathematicsElazigTurkey
  3. 3.Federal University DutseScience Faculty, Department of MathematicsJigawaNigeria
  4. 4.Cankaya UniversityDepartment of MathematicsAnkaraTurkey
  5. 5.Institute of Space SciencesBucharestRomania

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