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Fractional Analysis Of One-Dimensional Schrã–Dinger Model In The Context Of Caputo-Type Fractional Derivatives Based On Residual Power Series Method

Author

Listed:
  • MUHAMMAD NADEEM

    (School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, P. R. China)

  • YABIN SHAO

    (Research Institute of Microscale Optoelectronics, School of Jia Yang, Zhejiang Shuren University, Shaoxing 310009, P. R. China)

  • MRIM M. ALNFIAI

    (Department of Information Technology, College of Computers and Information Technology, Taif University, Taif P. O. Box 11099, Taif, 21944, Saudi Arabia)

  • WEJDAN DEEBANI

    (Department of Mathematics, College of Science & Arts, King Abdul Aziz University, Rabigh, Saudi Arabia)

  • MESHAL SHUTAYWI

    (Department of Mathematics, College of Science & Arts, King Abdul Aziz University, Rabigh, Saudi Arabia)

Abstract

This research presents a novel analytical approach to explore the fractional analysis of the one-dimensional time-fractional Schrödinger model (TFSM) using Caputo fractional derivatives. By integrating the Mohand transform (MT) with the residual power series method (RPSM), we develop the Mohand residual power series method (MT-RPSM) that provides results in the form of convergent series without assumptions on variables. Initially, we employ MT to reduce the fractional order, and then we transfer the fractional problem into the Mohand space formulation. Second, we use the RPSM concept to derive the iterative series formula for the Mohand space formulation. We analyze these findings using visual layouts to show the physical representation of the TFSM, which matches the precise results very well. The results indicate that the proposed technique is a reliable and practical method for identifying and analyzing various nonlinear models of physical phenomena.

Suggested Citation

  • Muhammad Nadeem & Yabin Shao & Mrim M. Alnfiai & Wejdan Deebani & Meshal Shutaywi, 2025. "Fractional Analysis Of One-Dimensional Schrã–Dinger Model In The Context Of Caputo-Type Fractional Derivatives Based On Residual Power Series Method," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:03:n:s0218348x24501391
    DOI: 10.1142/S0218348X24501391
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