Operational matrix for Atangana-Baleanu derivative based on Genocchi polynomials for solving FDEs

被引：51
作者：
Sadeghi, S. [1 ]
Jafari, H. [1 ,2 ]
Nemati, S. [1 ]
机构：
[1] Univ Mazandaran, Dept Math, Babol Sar, Iran
[2] Univ South Africa, Dept Math Sci, UNISA, ZA-0003 Pretoria, South Africa
来源：
CHAOS SOLITONS & FRACTALS | 2020年 / 135卷 / 135期
关键词：
Atangana-Baleanu derivative; Operational matrix; Non-singular kernel; Mittag-Leffler function; Genocchi polynomials; BURGERS-TYPE EQUATIONS; COMPOUND KDV-TYPE; NONLINEAR TERMS; WAVE SOLUTIONS;
D O I：
10.1016/j.chaos.2020.109736
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently, Atangana and Baleanu have defined a new fractional derivative which has a nonlocal and nonsingular kernel. It is called the Atangana-Baleanu derivative. In this paper we present a numerical technique to obtain solution of fractional differential equations containing Atangana-Baleanu derivative. For this purpose, we use the operational matrices based on Genocchi polynomials together with the collocation points which help us to reduce the problem to a system of algebraic equations. An error bound for the error of the operational matrix of the fractional derivative is introduced. Finally, some examples are given to illustrate the applicability and efficiency of the proposed method. (C) 2020 Elsevier Ltd. All rights reserved.
引用
收藏
页数：6
相关论文
共 31 条
[21]   EXACT-SOLUTIONS TO THE KDV-BURGERS EQUATION [J].
JEFFREY, A ;
MOHAMAD, MNB .
WAVE MOTION, 1991, 14 (04) :369-375
[22]  
Kim DS, 2015, ARS COMBINATORIA, V121, P403
[23]  
Kim T, 2017, J INEQUAL APPL, V2017, P19
[24]   Sums of finite products of Genocchi functions [J].
Kim, Taekyun ;
Kim, Dae San ;
Jang, Lee Chae ;
Jang, Gwan-Woo .
ADVANCES IN DIFFERENCE EQUATIONS, 2017,
[25]   Explicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order [J].
Li, B ;
Chen, Y ;
Zhang, HQ .
CHAOS SOLITONS & FRACTALS, 2003, 15 (04) :647-654
[26]   On the new properties of Caputo-Fabrizio operator and its application in deriving shifted Legendre operational matrix [J].
Loh, Jian Rong ;
Isah, Abdulnasir ;
Phang, Chang ;
Toh, Yoke Teng .
APPLIED NUMERICAL MATHEMATICS, 2018, 132 :138-153
[27]  
Losada J., 2015, PROGR FRACTIONAL DIF, V1, P87, DOI [DOI 10.12785/PFDA/010202, 10.12785/pfda/010202]
[28]   Solving FDEs with Caputo-Fabrizio derivative by operational matrix based on Genocchi polynomials [J].
Roshan, Sedighe Sadeghi ;
Jafari, Hossein ;
Baleanu, Dumitru .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (18) :9134-9141
[29]   Numerical solutions of the fractional Fisher's type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods [J].
Saad, K. M. ;
Khader, M. M. ;
Gomez-Aguilar, J. F. ;
Baleanu, Dumitru .
CHAOS, 2019, 29 (02)
[30]   A new operational matrix for solving fractional-order differential equations [J].
Saadatmandi, Abbas ;
Dehghan, Mehdi .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (03) :1326-1336
1234