Generalized theory of diffusive stresses associated with the time-fractional diffusion equation and nonlocal constitutive equations for the stress tensor

被引：4
|
作者：
Povstenko, Yuriy [1 ]
机构：
[1] Jan Dlugosz Univ Czestochowa, Fac Math & Nat Sci, Inst Math & Comp Sci, Al Armii Krajowej 13-15, PL-42200 Czestochowa, Poland
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 78卷 / 06期
关键词：
Diffusive stresses; Fractional calculus; Chemical potential; Nonlocal elasticity; Wright function; THERMODYNAMICS;
D O I：
10.1016/j.camwa.2016.02.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The theory of diffusive stresses based on the time-fractional diffusion equation with the Liouville-Caputo derivative is discussed. The diffusion process is characterized by the chemical potential tensor and the concentration tensor. Eliminating the chemical potential tensor and the concentration tensor from the constitutive equations for the stress tensor, the space-time-nonlocal equations for the mean stress and the deviatoric stress are obtained with the kernel being the Wright function. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1819 / 1825
页数：7
相关论文
共 50 条
  • [1] A class of time-fractional diffusion equations with generalized fractional derivatives
    Alikhanov, Anatoly A.
    Huang, Chengming
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 414
  • [2] The Cauchy problem for time-fractional linear nonlocal diffusion equations
    Sen Wang
    Xian-Feng Zhou
    Zeitschrift für angewandte Mathematik und Physik, 2023, 74
  • [3] Maximum principle for the generalized time-fractional diffusion equation
    Luchko, Yury
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 351 (01) : 218 - 223
  • [4] The Cauchy problem for time-fractional linear nonlocal diffusion equations
    Wang, Sen
    Zhou, Xian-Feng
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2023, 74 (04):
  • [5] NONLOCAL INITIAL BOUNDARY VALUE PROBLEM FOR THE TIME-FRACTIONAL DIFFUSION EQUATION
    Sadybekov, Makhmud
    Oralsyn, Gulaiym
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017,
  • [6] Generalized Boundary Conditions for the Time-Fractional Advection Diffusion Equation
    Povstenko, Yuriy
    ENTROPY, 2015, 17 (06) : 4028 - 4039
  • [7] Maximum Principles for a Class of Generalized Time-Fractional Diffusion Equations
    Shengda Zeng
    Stanisław Migórski
    Thien Van Nguyen
    Yunru Bai
    Fractional Calculus and Applied Analysis, 2020, 23 : 822 - 836
  • [8] MAXIMUM PRINCIPLES FOR A CLASS OF GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATIONS
    Zeng, Shengda
    Migorski, Stanislaw
    Van Thien Nguyen
    Bai, Yunru
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2020, 23 (03) : 822 - 836
  • [9] AN INVERSE TIME-DEPENDENT SOURCE PROBLEM FOR A TIME-FRACTIONAL DIFFUSION EQUATION WITH NONLOCAL
    Mihoubi, Farid
    Nouiri, Brahim
    MISKOLC MATHEMATICAL NOTES, 2024, 25 (02)
  • [10] Inverse source problem for a time-fractional diffusion equation with nonlocal boundary conditions
    Ismailov, Mansur I.
    Cicek, Muhammed
    APPLIED MATHEMATICAL MODELLING, 2016, 40 (7-8) : 4891 - 4899
12345