On spectral methods for solving variable-order fractional integro-differential equations

被引：26

作者：

Doha, E. H. ^{[1
]}

Abdelkawy, M. A. ^{[2
,3
]}

Amin, A. Z. M. ^{[4
]}

Lopes, Antonio M. ^{[5
]}

机构：

[1] Cairo Univ, Dept Math, Fac Sci, Giza, Egypt

[2] Al Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh, Saudi Arabia

[3] Beni Suef Univ, Dept Math, Fac Sci, Bani Suwayf, Egypt

[4] Canadian Int Coll, Inst Engn, Dept Basic Sci, Giza, Egypt

[5] Univ Porto, Fac Engn, UISPA LAETA INEGI, Porto, Portugal

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 03期

关键词：

Fractional calculus; Variable-order fractional operator; Spectral collocation method; Shifted Jacobi-Gauss-quadrature; GAUSS COLLOCATION METHOD; BOUNDARY-VALUE-PROBLEMS; NUMERICAL-SOLUTION; DIFFERENTIAL-EQUATIONS; EXISTENCE;

D O I：

10.1007/s40314-017-0551-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper applies the shifted Jacobi-Gauss collocation (SJ-G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann-Liouville fractional derivative, , and integral, , of variable order are combined, and the SJ-G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods.

引用

页码：3937 / 3950

页数：14

共 50 条

[21] Shifted fractional Legendre spectral collocation technique for solving fractional stochastic Volterra integro-differential equations
Doha, E. H.
Abdelkawy, M. A.
Amin, A. Z. M.
Lopes, Antonio M.
ENGINEERING WITH COMPUTERS, 2022, 38 (SUPPL 2) : 1363 - 1373
[22] A space–time spectral approximation for solving nonlinear variable-order fractional sine and Klein–Gordon differential equations
E. H. Doha
M. A. Abdelkawy
A. Z. M. Amin
António M. Lopes
Computational and Applied Mathematics, 2018, 37 : 6212 - 6229
[23] An efficient method for solving systems of fractional integro-differential equations
Momani, S.
Qaralleh, R.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 52 (3-4) : 459 - 470
[24] Fractional pseudospectral integration matrices for solving fractional differential, integral, and integro-differential equations
Tang, Xiaojun
Xu, Heyong
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 30 (1-3) : 248 - 267
[25] Haar wavelet method for solution of variable order linear fractional integro-differential equations
Amin, Rohul
Shah, Kamal
Ahmad, Hijaz
Ganie, Abdul Hamid
Abdel-Aty, Abdel-Haleem
Botmart, Thongchai
AIMS MATHEMATICS, 2022, 7 (04): : 5431 - 5443
[26] Numerical methods for fourth-order fractional integro-differential equations
Momani, Shaher
Noor, Muhammad Aslam
APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (01) : 754 - 760
[27] Fractional-order Euler functions for solving fractional integro-differential equations with weakly singular kernel
Wang, Yanxin
Zhu, Li
Wang, Zhi
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[28] Using ANNs Approach for Solving Fractional Order Volterra Integro-differential Equations
Jafarian, Ahmad
Rostami, Fariba
Golmankhaneh, Alireza K.
Baleanu, Dumitru
INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 2017, 10 (01) : 470 - 480
[29] Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations
Doha, Eid H.
Abdelkawy, Mohamed A.
Amin, Ahmed Z. M.
Baleanu, Dumitru
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2019, 24 (03): : 332 - 352
[30] Spectral collocation method for linear fractional integro-differential equations
Ma, Xiaohua
Huang, Chengming
APPLIED MATHEMATICAL MODELLING, 2014, 38 (04) : 1434 - 1448

← 1 2 3 4 5 →