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Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators

Author

Listed:
  • Ai-Min Yang
  • Zeng-Shun Chen
  • H. M. Srivastava
  • Xiao-Jun Yang

Abstract

We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.

Suggested Citation

  • 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, Hindawi, vol. 2013, pages 1-6, November.
    • Handle: RePEc:hin:jnlaaa:259125
    DOI: 10.1155/2013/259125
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    Cited by:

    1. 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).
    2. Xiao-Jun Yang & Jordan Hristov & H. M. Srivastava & Bashir Ahmad, 2014. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg‐de Vries Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Ai-Min Yang & Yu-Zhu Zhang & Xiao-Long Zhang, 2014. "The Nondifferentiable Solution for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow by Local Fractional Variational Iteration Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    4. Huixia Mo & Xin Sui, 2014. "Generalized s‐Convex Functions on Fractal Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. 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).
    6. Gong, Pan & Meftah, Badreddine & Xu, Hongyan & Budak, Hüseyin & Lakhdari, Abdelghani, 2025. "Exploring fractal–fractional integral inequalities: An extensive parametric study," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    7. Meng Li & Xiao-Feng Hui & Carlo Cattani & Xiao-Jun Yang & Yang Zhao, 2014. "Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    8. Lakhdari, Abdelghani & Budak, Hüseyin & Mlaiki, Nabil & Meftah, Badreddine & Abdeljawad, Thabet, 2025. "New insights on fractal–fractional integral inequalities: Hermite–Hadamard and Milne estimates," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).

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