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Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative

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  • Yong-Ju Yang
  • Liu-Qing Hua

Abstract

We propose the variational iteration transform method in the sense of local fractional derivative, which is derived from the coupling method of local fractional variational iteration method and differential transform method. The method reduces the integral calculation of the usual variational iteration computations to more easily handled differential operation. And the technique is more orderly and easier to analyze computing result as compared with the local fractional variational iteration method. Some examples are illustrated to show the feature of the presented technique.

Suggested Citation

  • Yong-Ju Yang & Liu-Qing Hua, 2014. "Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:760957
    DOI: 10.1155/2014/760957
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    References listed on IDEAS

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    1. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Hadi Karami & Azizollah Babakhani & Dumitru Baleanu, 2013. "Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with Delay," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    3. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Hadi Karami & Azizollah Babakhani & Dumitru Baleanu, 2013. "Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Shaher Momani, 2004. "Analytical Approximate Solutions Of Nonlinear Oscillators By The Modified Decomposition Method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 967-979.
    6. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    8. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, April.
    9. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, December.
    10. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, January.
    11. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    Cited by:

    1. Ahmed Farooq Qasim & Ekhlass S. AL-Rawi, 2018. "Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).

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