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New Reliable Algorithm for Fractional Harry Dym Equation

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Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 236))

Abstract

In this paper, a new reliable algorithm based on homotopy perturbation method using Laplace transform, named homotopy perturbation transform method (HPTM), is proposed to solve nonlinear fractional Harry Dym equation. The numerical solutions obtained by the HPTM show that the approach is easy to implement and computationally very attractive.

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References

  1. Hilfer, R. (ed.): Applications of Fractional Calculus in Physics, pp. 87–130. World Scientific Publishing Company, Singapore-New Jersey-Hong Kong (2000)

    Book  MATH  Google Scholar 

  2. Podlubny, I. (ed.): Fractional Differential Equations. Academic Press, New York (1999)

    MATH  Google Scholar 

  3. Caputo, M.: Elasticita e Dissipazione. Zani-Chelli, Bologna (1969)

    Google Scholar 

  4. Miller, K.S., Ross, B.: An Introduction to the fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

  5. Oldham, K.B., Spanier, J.: The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press, New York (1974)

    MATH  Google Scholar 

  6. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)

    MATH  Google Scholar 

  7. Mokhtari, R.: Exact solutions of the Harry-Dym equation. Commun. Theor. Phys. 55, 204–208 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kruskal, M.D., Moser, J.: Dynamical Systems, Theory and Applications, Lecturer Notes Physics, p. 310. Springer, Berlin (1975)

    Book  Google Scholar 

  9. Vosconcelos, G.L., Kaclanoff, L.P.: Stationary solution for the Saffman Taylor problem with surface tension. Phys. Rev. A 44, 6490–6495 (1991)

    Article  Google Scholar 

  10. Kumar, S., Tripathi, M.P., Singh O.P.: A fractional model of Harry Dym equation and its approximate solution. Ain Shams Eng. J. (2012). http://dx.doi.org/10.1016/j.asej.2012.07.001

  11. He, J.H.: Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178, 257–262 (1999)

    Article  MATH  Google Scholar 

  12. Khan, Y., Wu, Q.: Homotopy perturbation transform method for nonlinear equations using He’s polynomials. Comput. Math. Appl. 61(8), 1963–1967 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. Ghorbani, A.: Beyond adomian’s polynomials: He polynomials. Chaos Solitons Fractals 39, 1486–1492 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mohyud-Din, S.T., Noor, M.A., Noor, K.I.: Traveling wave solutions of seventh-order generalized KdV equation using He’s polynomials. Int. J. Nonlinear Sci. Numer. Simul. 10, 227–233 (2009)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, JaganNath Gupta Institute of Engineering and Technology, Jaipur, Rajasthan, 302022, India

    Devendra Kumar

  2. Department of Mathematics, Jagan Nath University, Village-Rampura, Tehsil-Chaksu, Jaipur, Rajasthan, 303901, India

    Jagdev Singh

Authors
  1. Devendra Kumar
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  2. Jagdev Singh
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Corresponding author

Correspondence to Devendra Kumar .

Editor information

Editors and Affiliations

  1. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    B. V. Babu

  2. Department of Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya Nagar

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  4. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, India

    Millie Pant

  5. Department of Applied Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  6. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    Kanad Ray

  7. Institute of Engineering and Technology, JK Lakshmipat University, Jaipur, Rajasthan, India

    Umesh Gupta

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Kumar, D., Singh, J. (2014). New Reliable Algorithm for Fractional Harry Dym Equation. In: Babu, B., et al. Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS 2012), December 28-30, 2012. Advances in Intelligent Systems and Computing, vol 236. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1602-5_28

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  • DOI: https://doi.org/10.1007/978-81-322-1602-5_28

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1601-8

  • Online ISBN: 978-81-322-1602-5

  • eBook Packages: EngineeringEngineering (R0)

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