Numerical Solution of Variable-Order Time Fractional Weakly Singular Partial Integro-Differential Equations with Error Estimation

被引：15

作者：

Dehestani, Haniye ^{[1
]}

Ordokhani, Yadollah ^{[1
]}

Razzaghi, Mohsen ^{[2
]}

机构：

[1] Alzahra Univ, Fac Math Sci, Dept Math, Tehran, Iran

[2] Mississippi State Univ, Dept Math & Stat, Starkville, MS 39762 USA

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2020年 / 25卷 / 04期

关键词：

variable-order fractional partial integro-differential equations; weakly singular kernel; Legendre-Laguerre functions; pseudo-operational matrix; CONVERGENCE; DYNAMICS; VAN;

D O I：

10.3846/mma.2020.11692

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we apply Legendre-Laguerre functions (LLFs) and collocation method to obtain the approximate solution of variable-order time-fractional partial integro-differential equations (VO-TF-PIDEs) with the weakly singular kernel. For this purpose, we derive the pseudo-operational matrices with the use of the transformation matrix. The collocation method and pseudo-operational matrices transfer the problem to a system of algebraic equations. Also, the error analysis of the proposed method is given. We consider several examples to illustrate the proposed method is accurate.

引用

页码：680 / 701

页数：22

共 37 条

[11] Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation [J].

Diaz, G. ;

Coimbra, C. F. M. .

NONLINEAR DYNAMICS, 2009, 56 (1-2) :145-157

[12] SPLINE COLLOCATION METHODS FOR A CLASS OF HYPERBOLIC PARTIAL INTEGRODIFFERENTIAL EQUATIONS [J].

FAIRWEATHER, G .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (02) :444-460

[13]

Hormander Lars, 1990, The Analysis of Linear Partial Differential Operators: Distribution Theory and Fourier Analysis, V2nd, DOI [10.1007/978-3-642-61497-2, DOI 10.1007/978-3-642-61497-2]

[14] Control of damping oscillations by fractional differential operator with time-dependent order [J].

Ingman, D ;

Suzdalnitsky, J .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (52) :5585-5595

[15] A numerical method for solving the time variable fractional order mobile-immobile advection-dispersion model [J].

Jiang, Wei ;

Liu, Na .

APPLIED NUMERICAL MATHEMATICS, 2017, 119 :18-32

[16] Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation [J].

Lin, R. ;

Liu, F. ;

Anh, V. ;

Turner, I. .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 212 (02) :435-445

[17]

Linz P., 1985, Analytical and numerical methods for Volterra equations, DOI 10.1137/1.9781611970852

[18] Time discretization via Laplace transformation of an integro-differential equation of parabolic type [J].

McLean, W ;

Sloan, IH ;

Thomée, V .

NUMERISCHE MATHEMATIK, 2006, 102 (03) :497-522

[19] An integro quadratic spline approach for a class of variable-order fractional initial value problems [J].

Moghaddam, B. P. ;

Machado, J. A. T. ;

Behforooz, H. .

CHAOS SOLITONS & FRACTALS, 2017, 102 :354-360

[20] A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations [J].

Moghaddam, B. P. ;

Machado, J. A. T. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) :1262-1269

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