New analysis and application of fractional order Schrodinger equation using with Atangana-Batogna numerical scheme

被引：3

作者：

Akcetin, Eyup ^{[1
]}

Koca, Ilknur ^{[2
]}

Kilic, Muhammet Burak ^{[3
]}

机构：

[1] Mugla Sitki Kocman Univ, Seydikemer Appl Sci Sch, Dept Accounting & Financial Management, Mugla, Turkey

[2] Mehmet Akif Ersoy Univ, Dept Math, Fac Sci, TR-15100 Burdur, Turkey

[3] Mehmet Akif Ersoy Univ, Fac Econ & Adm Sci, Dept Business Adm, Burdur, Turkey

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 37卷 / 01期

关键词：

fractional order differentiation; Schrodinger equation; numerical scheme; MODEL;

D O I：

10.1002/num.22525

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：196 / 209

页数：14

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