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The Approximate Solutions of Three‐Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator

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  • Hassan Kamil Jassim

Abstract

We used the local fractional variational iteration transform method (LFVITM) coupled by the local fractional Laplace transform and variational iteration method to solve three‐dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method.

Suggested Citation

  • Hassan Kamil Jassim, 2016. "The Approximate Solutions of Three‐Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:2913539
    DOI: 10.1155/2016/2913539
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    References listed on IDEAS

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    1. Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, June.
    2. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, January.
    3. Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. 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.
    5. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Yang, Xiao-Jun & Tenreiro Machado, J.A. & Srivastava, H.M., 2016. "A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 143-151.
    7. 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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