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An efficient analytical scheme with convergence analysis for computational study of local fractional Schrödinger equations

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  • Dubey, Ved Prakash
  • Singh, Jagdev
  • Alshehri, Ahmed M.
  • Dubey, Sarvesh
  • Kumar, Devendra

Abstract

In this paper, we present a newly proposed local fractional method pertaining to the local fractional Sumudu transform (LFST) for computational study of local fractional Schrödinger’s equations (LFSEs). The error analysis for the present method is also discussed here. The uniqueness and convergence analyses for the solution obtained by using the proposed scheme are also established. The numerical simulations for achieved results have been performed for different orders of a local fractional derivative. The results depict that the proposed method efficiently provides the solution for given equations in a smooth manner.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:296-318
    DOI: 10.1016/j.matcom.2022.01.012
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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.
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    4. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Fethi Bin Muhammed Belgacem & Ahmed Abdullatif Karaballi & Shyam L. Kalla, 2003. "Analytical investigations of the Sumudu transform and applications to integral production equations," Mathematical Problems in Engineering, Hindawi, vol. 2003, pages 1-16, January.
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    7. 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.
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    10. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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    13. 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, Hindawi, vol. 2013, pages 1-5, September.
    14. 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, Hindawi, vol. 2014, pages 1-7, June.
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