Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

被引：89

作者：

Ali, Khalid K. ^{[1
]}

Abd El Salam, Mohamed A. ^{[1
]}

Mohamed, Emad M. H. ^{[1
]}

Samet, Bessem ^{[2
]}

Kumar, Sunil ^{[3
]}

Osman, M. S. ^{[4
]}

机构：

[1] Al Azhar Univ, Fac Sci, Dept Math, Cairo, Egypt

[2] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

[3] Natl Inst Technol, Dept Math, Jamshedpur 831014, Jharkhand, India

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

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Chebyshev collocation method; Nonlinear fractional integro-differential equations; Functional argument; Caputo fractional derivatives; COLLOCATION METHOD; FUNDAMENTAL-SOLUTIONS; SYSTEMS; MODEL; SOLITONS;

D O I：

10.1186/s13662-020-02951-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of delay, proportional delay, and advanced non-linear arbitrary order Fredholm-Volterra integro-differential equations. Spectral collocation method is extended to study this problem as a matrix discretization scheme, where the fractional derivatives are characterized in the Caputo sense. The collocation method transforms the given equation and conditions to an algebraic nonlinear system of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. The introduced operational matrix of derivatives includes arbitrary order derivatives and the operational matrix of ordinary derivative as a special case. To the best of authors' knowledge, there is no other work discussing this point. Numerical test examples are given, and the achieved results show that the recommended method is very effective and convenient.

引用

页数：23