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Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

Author

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  • Jagdev Singh
  • Devendra Kumar
  • A. Kılıçman

Abstract

A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.

Suggested Citation

  • Jagdev Singh & Devendra Kumar & A. Kılıçman, 2013. "Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, February.
    • Handle: RePEc:hin:jnlaaa:934060
    DOI: 10.1155/2013/934060
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    Cited by:

    1. Khirsariya, Sagar R. & Chauhan, Jignesh P. & Rao, Snehal B., 2024. "A robust computational analysis of residual power series involving general transform to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 168-186.
    2. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
    4. Korkmaz, Alper, 2017. "Exact solutions of space-time fractional EW and modified EW equations," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 132-138.

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