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New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations

Author

Listed:
  • Hayman Thabet

    (Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India)

  • Subhash Kendre

    (Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India)

  • Dimplekumar Chalishajar

    (Department of Applied Mathematics, Virginia Military Institute, Lexington, VA 24450, USA)

Abstract

This paper introduces a new analytical technique (NAT) for solving a system of nonlinear fractional partial differential equations (NFPDEs) in full general set. Moreover, the convergence and error analysis of the proposed technique is shown. The approximate solutions for a system of NFPDEs are easily obtained by means of Caputo fractional partial derivatives based on the properties of fractional calculus. However, analytical and numerical traveling wave solutions for some systems of nonlinear wave equations are successfully obtained to confirm the accuracy and efficiency of the proposed technique. Several numerical results are presented in the format of tables and graphs to make a comparison with results previously obtained by other well-known methods.

Suggested Citation

  • Hayman Thabet & Subhash Kendre & Dimplekumar Chalishajar, 2017. "New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:47-:d:113170
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    2. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    3. 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.
    4. Sun, HongGuang & Chen, Wen & Li, Changpin & Chen, YangQuan, 2010. "Fractional differential models for anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2719-2724.
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