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

[1]

Abdelkawy MA, 2015, ROM REP PHYS, V67, P773

[2] Numerical solution of variable-order fractional integro-partial differential equations via Sinc collocation method based on single and double exponential transformations [J].

Babaei, A. ;

Moghaddam, B. P. ;

Banihashemi, S. ;

Machado, J. A. T. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 82 (82)

[3] New study of weakly singular kernel fractional fourth-order partial integro-differential equations based on the optimum q-homotopic analysis method [J].

Baleanu, Dumitru ;

Darzi, Rahmat ;

Agheli, Bahram .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 320 :193-201

[4]

Behzadi SS., 2012, COMMUNICATIONS NUMER, V2012, P1, DOI DOI 10.5899/2012/CNA-00108

[5]

Canuto C., 2006, SCIENTIF COMPUT

[6] Mechanics with variable-order differential operators [J].

Coimbra, CFM .

ANNALEN DER PHYSIK, 2003, 12 (11-12) :692-703

[7] Fractional-order Legendre-Laguerre functions and their applications in fractional partial differential equations [J].

Dehestani, H. ;

Ordokhani, Y. ;

Razzaghi, M. .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 336 :433-453

[8] Hybrid functions for numerical solution of fractional Fredholm-Volterra functional integro-differential equations with proportional delays [J].

Dehestani, Haniye ;

Ordokhani, Yadollah ;

Razzaghi, Mohsen .

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING-ELECTRONIC NETWORKS DEVICES AND FIELDS, 2019, 32 (05)

[9] Application of the modified operational matrices in multiterm variable-order time-fractional partial differential equations [J].

Dehestani, Haniye ;

Ordokhani, Yadollah ;

Razzaghi, Mohsen .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (18) :7296-7313

[10] Solution of a partial integro-differential equation arising from viscoelasticity [J].

Dehghan, M .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2006, 83 (01) :123-129

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