Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives

被引：1
|
作者：
Nicole Heymans
Igor Podlubny
机构：
[1] Université Libre de Bruxelles,Physique des Matériaux de Synthèse
[2] Technical University of Kosice,B.E.R.G. Faculty
来源：
Rheologica Acta | 2006年 / 45卷
关键词：
Impulse Response; Fractional Order; Fractional Derivative; Fractional Differential Equation; Caputo Derivative;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
On a series of examples from the field of viscoelasticity we demonstrate that it is possible to attribute physical meaning to initial conditions expressed in terms of Riemann–Liouville fractional derivatives, and that it is possible to obtain initial values for such initial conditions by appropriate measurements or observations.
引用
收藏
页码：765 / 771
页数：6
相关论文
共 50 条
  • [1] Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    Heymans, Nicole
    Podlubny, Igor
    [J]. RHEOLOGICA ACTA, 2006, 45 (05) : 765 - 771
  • [2] RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL BOUNDARY CONDITIONS
    Ahmad, Bashir
    Nieto, Juan J.
    [J]. FIXED POINT THEORY, 2012, 13 (02): : 329 - 336
  • [3] Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives
    Li Kexue
    Peng Jigen
    Jia Junxiong
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (02) : 476 - 510
  • [4] Riemann-Liouville fractional differential equations with Hadamard fractional integral conditions
    Tariboon, Jessada
    Ntouyas, Sotiris K.
    Thiramanus, Phollakrit
    [J]. INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2016, 54 (01): : 119 - 134
  • [5] An approximate solution method for ordinary fractional differential equations with the Riemann-Liouville fractional derivatives
    Lukashchuk, S. Yu.
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (02) : 390 - 400
  • [6] Solvability of BVPs for impulsive fractional differential equations involving the Riemann-Liouville fractional derivatives
    Liu, Yuji
    [J]. STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2018, 63 (01): : 79 - 108
  • [7] Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann-Liouville Sense
    Luchko, Yuri
    [J]. MATHEMATICS, 2022, 10 (06)
  • [8] Nonlocal Hadamard fractional integral conditions for nonlinear Riemann-Liouville fractional differential equations
    Jessada Tariboon
    Sotiris K Ntouyas
    Weerawat Sudsutad
    [J]. Boundary Value Problems, 2014
  • [9] Nonlocal Hadamard fractional integral conditions for nonlinear Riemann-Liouville fractional differential equations
    Tariboon, Jessada
    Ntouyas, Sotiris K.
    Sudsutad, Weerawat
    [J]. BOUNDARY VALUE PROBLEMS, 2014,
  • [10] Fractional differential equations of motion in terms of combined Riemann-Liouville derivatives
    Zhang Yi
    [J]. CHINESE PHYSICS B, 2012, 21 (08)
12345