New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme

In this work, an analytical approximation to the solution of Schrodinger equation has been provided. The fractional derivative used in this equation is the Caputo derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on the power law. While solving...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2021-01, Vol.37 (1), p.196-209
Main Authors: Akçetin, Eyüp, Koca, Ilknur, Kiliç, Muhammet Burak
Format: Article
Language:English
Subjects:
fractional order differentiation
Mathematical models
Nonlinear equations
Numerical methods
numerical scheme
Schrodinger equation
Schrödinger equation
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Summary:In this work, an analytical approximation to the solution of Schrodinger equation has been provided. The fractional derivative used in this equation is the Caputo derivative. The existence and uniqueness conditions of solutions for the proposed model are derived based on the power law. While solving the fractional order Schrodinger equation, Atangana–Batogna numerical method is presented for fractional order equation. We obtain an efficient recurrence relation for solving these kinds of equations. To illustrate the usefulness of the numerical scheme, the numerical simulations are presented. The results show that the numerical scheme is very effective and simple.
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22525