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Recent Advances in Mathematical Sciences pp 37–44Cite as

Modified Homotopy Perturbation Method for Fredholm–Volterra Integro-Differential Equation

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Abstract

In this paper, consider a linear Fredholm–Volterro integro-differential equation (FVIDE) of the third kind has derivative of order m where m is positive integer. This type of integral has been solved by using modified homotopy perturbation method (HPM) to get approximate solutions. In this modification, selective functions and unknown parameters are introduced to help us obtain only two-step iterations. This proposed method could avoid common problems such as complex and long calculations. It is found that modified HPM is a semi-analytical method and easy to apply for solving FVIDE. Numerical examples are given to present the efficiency and reliability of the propose method.

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Acknowledgments

This work was supported by Universiti Putra Malaysia under Research Grant Universiti Putra Malaysia (Putra Grant 2014). The project code is GP-i/2014/9442300. Authors are grateful for the sponsor and financial support of the Research Management Center, Universiti Putra Malaysia.

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Authors and Affiliations

  1. Faculty of Science, Departments of Mathematics, Universiti Putra Malaysia (UPM), Serdang, Selangor, Malaysia

    F. S. Zulkarnain & F. Ismail

  2. Faculty of Science and Technology, Universiti Sains ISlam Malaysia (USIM), Nilai, Negeri Sembilan, Malaysia

    Z. K. Eshkuvatov

  3. Institute for Mathematical Research, Universiti Putra Malaysia (UPM), Serdang, Selangor, Malaysia

    N. M. A. Nik Long

Authors
  1. F. S. Zulkarnain
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  2. Z. K. Eshkuvatov
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  3. N. M. A. Nik Long
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  4. F. Ismail
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Corresponding author

Correspondence to F. S. Zulkarnain .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University Putra Malaysia, Serdang, Malaysia

    Adem Kılıçman

  2. University of Victoria, Victoria, Canada

    Hari M. Srivastava

  3. Aligarh Muslim University, Aligarh, India

    M. Mursaleen

  4. Universiti Putra Malaysia, Serdang, Malaysia

    Zanariah Abdul Majid

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© 2016 Springer Science+Business Media Singapore

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Zulkarnain, F.S., Eshkuvatov, Z.K., Nik Long, N.M.A., Ismail, F. (2016). Modified Homotopy Perturbation Method for Fredholm–Volterra Integro-Differential Equation. In: Kılıçman, A., Srivastava, H., Mursaleen, M., Abdul Majid, Z. (eds) Recent Advances in Mathematical Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-10-0519-0_4

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