On a class of non-linear delay distributed order fractional diffusion equations

被引：51

作者：

Pimenov, V. G. ^{[1
,2
]}

Hendy, A. S. ^{[2
]}

De Staelen, R. H. ^{[3
]}

机构：

[1] RAS, Inst Math & Mech, Ural Branch, 16 St S Kovalevskoy, Ekaterinburg 620000, Russia

[2] Ural Fed Univ, Inst Math & Comp Sci, Dept Computat Math, Ul Mira 19, Ekaterinburg 620002, Russia

[3] Univ Ghent, Res Grp Numer Anal & Math Modeling NaM2, Dept Math Anal, B-9000 Ghent, Belgium

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 318卷

关键词：

Distributed order fractional partial differential equations; Difference scheme; Discrete energy method; Delay partial differential equations; Convergence; Stability; DIFFERENCE-SCHEMES; NUMERICAL-SOLUTION; WAVE EQUATION; MODEL;

D O I：

10.1016/j.cam.2016.02.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a numerical scheme for a class of non-linear time delay fractional diffusion equations with distributed order in time. This study covers the unique solvability, convergence and stability of the resulted numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(tau + (Delta alpha)(4) + h(4)) in L-infinity-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：433 / 443

页数：11

共 38 条

[1]

[Anonymous], 2003, Numerical Methods for Delay Differential Equations

[2]

[Anonymous], 2012, Series on Complexity, Nonlinearity and Chaos, DOI 10.1142/10044

[3]

[Anonymous], 2001, FRACT CALC APPL ANAL

[4]

Ashyraliev A., 1994, OPERATOR THEORY ADV, V69

[5] On a nonlinear distributed order fractional differential equation [J].

Atanackovic, Teodor M. ;

Oparnica, Ljubica ;

Pihpovic, Stevan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 328 (01) :590-608

[6] On a fractional distributed-order oscillator [J].

Atanackovic, TM ;

Budincevic, M ;

Pilipovic, S .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (30) :6703-6713

[7] A generalized model for the uniaxial isothermal deformation of a viscoelastic body [J].

Atanackovic, TM .

ACTA MECHANICA, 2002, 159 (1-4) :77-86

[8] Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod [J].

Atanackovica, T. M. ;

Pilipovic, S. ;

Zorica, D. .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2011, 49 (02) :175-190

[9] A THEORETICAL BASIS FOR THE APPLICATION OF FRACTIONAL CALCULUS TO VISCOELASTICITY [J].

BAGLEY, RL ;

TORVIK, PJ .

JOURNAL OF RHEOLOGY, 1983, 27 (03) :201-210

[10]

Caputo M, 2001, Fract Calc Appl Anal, V4, P421

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