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
收藏
页码：8345 / 8349
页数：5
相关论文
共 50 条
  • [41] Time-fractional extensions of the Liouville and Zwanzig equations
    Lukashchuk, Stanislav Yu.
    CENTRAL EUROPEAN JOURNAL OF PHYSICS, 2013, 11 (06): : 740 - 749
  • [42] A class of time-fractional diffusion equations with generalized fractional derivatives
    Alikhanov, Anatoly A.
    Huang, Chengming
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 414
  • [43] On the time-fractional Navier-Stokes equations
    Zhou, Yong
    Peng, Li
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) : 874 - 891
  • [44] Advances in fractional differential equations (IV): Time-fractional PDEs
    Zhou, Yong
    Feckan, Michal
    Liu, Fawang
    Tenreiro Machado, J. A.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) : 873 - 873
  • [45] A generalization of Duhamel's principle for differential equations of fractional order
    Umarov, S. R.
    Saidamatov, E. M.
    DOKLADY MATHEMATICS, 2007, 75 (01) : 94 - 96
  • [46] Numerical Solution of Time-Fractional Schrodinger Equation by Using FDM
    Serik, Moldir
    Eskar, Rena
    Huang, Pengzhan
    AXIOMS, 2023, 12 (09)
  • [47] FEYNMAN PATH FORMULA FOR THE TIME FRACTIONAL SCHRODINGER EQUATION
    Emamirad, Hassan
    Rougirel, Arnaud
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2020, 13 (12): : 3391 - 3400
  • [48] Analytic and Numerical Solutions of Time-Fractional Linear Schrodinger Equation
    Edeki, S. O.
    Akinlabi, G. O.
    Adeosun, S. A.
    COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2016, 7 (01): : 1 - 10
  • [49] Solving the time-fractional Schrodinger equation by Krylov projection methods
    Garrappa, Roberto
    Moret, Igor
    Popolizio, Marina
    JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 115 - 134
  • [50] A generalization of Duhamel’s principle for differential equations of fractional order
    S. R. Umarov
    E. M. Saidamatov
    Doklady Mathematics, 2007, 75 : 94 - 96
12345