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Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

Author

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  • Ai-Min Yang
  • Xiao-Jun Yang
  • Zheng-Biao Li

Abstract

We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:351057
    DOI: 10.1155/2013/351057
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    Citations

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    Cited by:

    1. 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).
    2. Kumar, Devendra & Dubey, Ved Prakash & Dubey, Sarvesh & Singh, Jagdev & Alshehri, Ahmed Mohammed, 2023. "Computational analysis of local fractional partial differential equations in realm of fractal calculus," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Guang-Sheng Chen & H. M. Srivastava & Pin Wang & Wei Wei, 2014. "Some Further Generalizations of Hölder′s Inequality and Related Results on Fractal Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Ai-Min Yang & Yu-Zhu Zhang & Carlo Cattani & Gong-Nan Xie & Mohammad Mehdi Rashidi & Yi-Jun Zhou & Xiao-Jun Yang, 2014. "Application of Local Fractional Series Expansion Method to Solve Klein‐Gordon Equations on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Yang Zhao & De-Fu Cheng & Xiao-Jun Yang, 2013. "Approximation Solutions for Local Fractional Schrödinger Equation in the One‐Dimensional Cantorian System," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    6. Dubey, Ved Prakash & Singh, Jagdev & Alshehri, Ahmed M. & Dubey, Sarvesh & Kumar, Devendra, 2022. "An efficient analytical scheme with convergence analysis for computational study of local fractional Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 296-318.
    7. Nur Alam & Fethi Bin Muhammad Belgacem, 2016. "Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation," Mathematics, MDPI, vol. 4(1), pages 1-13, February.
    8. Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    9. Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Xiao-Jun Yang & Dumitru Baleanu & H. M. Srivastava & J. A. Tenreiro Machado, 2013. "On Local Fractional Continuous Wavelet Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Ai-Min Yang & Zeng-Shun Chen & H. M. Srivastava & Xiao-Jun Yang, 2013. "Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    12. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    13. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    14. 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).

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