New numerical analysis of Riemann-Liouville time-fractional Schrodinger with power, exponential decay, and Mittag-Leffler laws

被引：5

作者：

Alkahtani, Badr Saad T. ^{[1
]}

Koca, Ilknur ^{[2
]}

Atangana, Abdon ^{[3
]}

机构：

[1] King Saud Univ, Dept Math, Colle Sci, POB 1142, Riyadh 11989, Saudi Arabia

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

[3] Univ Free State, Inst Groundwater Studies, Fac Nat & Agr Sci, ZA-9300 Bloemfontein, South Africa

来源：

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS | 2017年 / 10卷 / 08期

关键词：

Power law; exponential decay law; Mittag-Leffler law; numerical scheme; Schrodinger equation; DIFFUSION EQUATION;

D O I：

10.22436/jnsa.010.08.18

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The mathematical equation that describes how the quantum state of a quantum system changes during time was considered within the framework of fractional differentiation with three different derivatives in Riemann-Liouville sense. The fractional derivatives used in this work are constructed based on power, exponential decay, and Mittag-Leffler law. A new numerical scheme for fractional derivative in Riemann-Liouville sense is presented and used to solve numerically the Schrodinger equation. The stability analysis of each model is presented in detail. (C) 2017 All rights reserved.

引用

页码：4231 / 4243

页数：13

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