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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.
    2. Hossein Jafari & Hassan Kamil Jassim & Dumitru Baleanu & Yu-Ming Chu, 2021. "On The Approximate Solutions For A System Of Coupled Korteweg–De Vries Equations With Local Fractional Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-7, August.
    3. Fethi Bin Muhammed Belgacem & Ahmed Abdullatif Karaballi, 2006. "Sumudu transform fundamental properties investigations and applications," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-23, May.
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    6. 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).
    7. Xiao-Jun Yang & Dumitru Baleanu & J. A. Tenreiro Machado, 2013. "Systems of Navier-Stokes Equations on Cantor Sets," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, June.
    8. 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).
    9. Xiao-Jing Ma & H. M. Srivastava & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-6, July.
    10. 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.
    11. Hassan Kamil Jassim & Canan Ünlü & Seithuti Philemon Moshokoa & Chaudry Masood Khalique, 2015. "Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, June.
    12. 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.
    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, Hindawi, vol. 2014, pages 1-7, June.
    14. 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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