A COMPUTATIONAL APPROACH FOR THE SOLUTION OF A CLASS OF VARIABLE-ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS

被引：56

作者：

Moghaddam, Behrouz Parsa ^{[1
]}

Tenreiro Machado, Jose Antonio ^{[2
]}

机构：

[1] Islamic Azad Univ, Lahijan Branch, Dept Math, Lahijan, Iran

[2] Inst Engn, Dept Elect Engn, Rua Dr Antonio Bernardino de Almeida 431, P-4249015 Oporto, Portugal

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2017年 / 20卷 / 04期

关键词：

variable-order fractional calculus; spline approximation; finite difference approximation; convergence order; weakly singular integro-differential equation; NUMERICAL APPROXIMATIONS; DIFFERENTIAL-EQUATION; DERIVATIVES; ALGORITHMS; CALCULUS; SYSTEMS; SCW;

D O I：

10.1515/fca-2017-0053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new computational approach for approximating of variable-order fractional derivatives is proposed. The technique is based on piecewise cubic spline interpolation. The method is extended to a class of nonlinear variable-order fractional integro-differential equation with weakly singular kernels. Illustrative examples are discussed, demonstrating the performance of the numerical scheme.

引用

页码：1023 / 1042

页数：20

共 50 条

[31] Error analysis of arbitrarily high-order stepping schemes for fractional integro-differential equations with weakly singular kernels
Al-Shara, Safwan
Awawdeh, Fadi
Rawashdeh, Edris
Alsayyed, Omar
Alshorman, Rafat
NONLINEAR ENGINEERING - MODELING AND APPLICATION, 2024, 13 (01):
[32] Bernoulli Polynomials Collocation for Weakly Singular Volterra Integro-Differential Equations of Fractional Order
Azodi, Haman Deilami
Yaghouti, Mohammad Reza
FILOMAT, 2018, 32 (10) : 3623 - 3635
[33] The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays
Brunner, H
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2006, 5 (02) : 261 - 276
[34] Bernstein series solution of a class of linear integro-differential equations with weakly singular kernel
Isik, Osman Rasit
Sezer, Mehmet
Guney, Zekeriya
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (16) : 7009 - 7020
[35] A spectral approach to non-linear weakly singular fractional integro-differential equations
Amin Faghih
Magda Rebelo
Fractional Calculus and Applied Analysis, 2023, 26 : 370 - 398
[36] An efficient numerical approach to solve a class of variable-order fractional integro-partial differential equations
Babaei, Afshin
Banihashemi, Seddigheh
Cattani, Carlo
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2021, 37 (01) : 674 - 689
[37] An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels
Zheng Ma
Chengming Huang
Numerical Algorithms, 2023, 92 : 2377 - 2404
[38] An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels
Ma, Zheng
Huang, Chengming
NUMERICAL ALGORITHMS, 2023, 92 (04) : 2377 - 2404
[39] An hp-version of the discontinuous Galerkin method for fractional integro-differential equations with weakly singular kernels
Chen, Yanping
Chen, Zhenrong
Huang, Yunqing
BIT NUMERICAL MATHEMATICS, 2024, 64 (03)
[40] 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,

← 1 2 3 4 5 →