Duhamel's formula for time-fractional Schrodinger equations

被引：30

作者：

Zhou, Yong ^{[1
]}

Peng, Li ^{[1
]}

Huang, Yunqing ^{[1
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 17期

基金：

中国国家自然科学基金;

关键词：

Caputo fractional derivative; Duhamel's formula; Schrodinger equations;

D O I：

10.1002/mma.5222

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the time-fractional order Schrodinger equation that is a fundamental equation in fractional quantum mechanics. By using the spectral theorem, we prove Duhamel's formula and give some properties of solution operators, which can be used to study the local existence and the global existence of time-fractional Schrodinger equations on a Hilbert space.

引用

页码：8345 / 8349

页数：5

共 29 条

[1]

Aliyu AI, 2018, WAVE RANDOM COMPLEX, P1

[2]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[3]

[Anonymous], FRACTIONAL EVOLUTION

[4]

[Anonymous], 2006, Journal of the Electrochemical Society

[5] Application of Fixed Point Theorem for Stability Analysis of a Nonlinear Schrodinger with Caputo-Liouville Derivative [J].

Atangana, Abdon ;

Baleanu, Dumitru .

FILOMAT, 2017, 31 (08) :2243-2248

[6] The Motion of a Bead Sliding on a Wire in Fractional Sense [J].

Baleanu, D. ;

Jajarmi, A. ;

Asad, J. H. ;

Blaszczyk, T. .

ACTA PHYSICA POLONICA A, 2017, 131 (06) :1561-1564

[7] A New Formulation of the Fractional Optimal Control Problems Involving Mittag-Leffler Nonsingular Kernel [J].

Baleanu, Dumitru ;

Jajarmi, Amin ;

Hajipour, Mojtaba .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2017, 175 (03) :718-737

[8] Time fractional Schrodinger equation: Fox's H-functions and the effective potential [J].

Bayin, Selcuk S. .

JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (01)

[9]

Cazenave T, 2003, COURANT LECT NOTES

[10] Schrodinger equation involving fractional operators with non-singular kernel [J].

Gomez-Aguilar, J. F. ;

Baleanu, Dumitru .

JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS, 2017, 31 (07) :752-761

← 1 2 3 →