Maximum principle for the generalized time-fractional diffusion equation

被引：259
|
作者：
Luchko, Yury [1 ]
机构：
[1] Tech Univ Appl Sci Berlin, Dept Math 2, D-13353 Berlin, Germany
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 351卷 / 01期
关键词：
Caputo-Dzherbashyan fractional derivative; Time-fractional diffusion equation; Initial-boundary-value problems; Maximum principle; Uniqueness theorem; CAUCHY-PROBLEM;
D O I：
10.1016/j.jmaa.2008.10.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper, a maximum principle for the generalized time-fractional diffusion equation over an open bounded domain G x (0. T). G subset of R-n is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Caputo-Dzherbashyan fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial-boundary-value problem for the generalized time-fractional diffusion equation possesses at most one classical solution and this Solution continuously depends on the initial and boundary conditions. (c) 2008 Elsevier Inc. All rights reserved.
引用
收藏
页码：218 / 223
页数：6
相关论文
共 50 条
  • [21] Generalized Tikhonov method for the final value problem of time-fractional diffusion equation
    Zhang, Hongwu
    Zhang, Xiaoju
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2017, 94 (01) : 66 - 78
  • [22] Identifying a diffusion coefficient in a time-fractional diffusion equation
    Wei, T.
    Li, Y. S.
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2018, 151 : 77 - 95
  • [23] Generalized Tikhonov methods for an inverse source problem of the time-fractional diffusion equation
    Ma, Yong-Ki
    Prakash, P.
    Deiveegan, A.
    CHAOS SOLITONS & FRACTALS, 2018, 108 : 39 - 48
  • [24] On the solution of generalized time-fractional telegraphic equation
    Albalawi, Kholoud Saad
    Shokhanda, Rachana
    Goswami, Pranay
    APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, 2023, 31 (01):
  • [25] Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel
    Kedia, Nikki
    Alikhanov, Anatoly A.
    Singh, Vineet Kumar
    APPLIED NUMERICAL MATHEMATICS, 2022, 172 : 546 - 565
  • [26] A numerical approach for nonlinear time-fractional diffusion equation with generalized memory kernel
    Seal, Aniruddha
    Natesan, Srinivasan
    NUMERICAL ALGORITHMS, 2024, 97 (02) : 539 - 565
  • [27] Time-fractional diffusion equation for signal smoothing
    Li, Yuanlu
    Liu, Fawang
    Turner, Ian W.
    Li, Tao
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 326 : 108 - 116
  • [28] Time-fractional diffusion equation with ψ-Hilfer derivative
    Vieira, Nelson
    Rodrigues, M. Manuela
    Ferreira, Milton
    COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (06):
  • [29] A backward problem for the time-fractional diffusion equation
    Al-Jamal, Mohammad F.
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (07) : 2466 - 2474
  • [30] Uniqueness of the potential in a time-fractional diffusion equation
    Jing, Xiaohua
    Peng, Jigen
    JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2023, 31 (04): : 467 - 477
12345