FRACTIONAL ANALYSIS OF ONE-DIMENSIONAL SCHRÖDINGER MODEL IN THE CONTEXT OF CAPUTO-TYPE FRACTIONAL DERIVATIVES BASED ON RESIDUAL POWER SERIES METHOD

Muhammad Nadeem, Yabin Shao, Mrim M. Alnfiai, Wejdan Deebani and Meshal Shutaywi
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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

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-16

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.

Keywords: Mohand Transform; Residual Power Series Method; Schrödinger Model; Fractional Analysis; Convergent Series (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501391

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