Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations

被引：25

作者：

Mohammed, Pshtiwan Othman ^{[1
]}

Machado, Jose Antonio Tenreiro ^{[2
]}

Guirao, Juan L. G. ^{[3
,4
]}

Agarwal, Ravi P. ^{[5
]}

机构：

[1] Univ Sulaimani, Coll Educ, Dept Math, Sulaimani 46001, Kurdistan Regio, Iraq

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

[3] Tech Univ Cartagena, Hosp Marina, Dept Appl Math & Stat, Cartagena 30203, Spain

[4] King Abdulaziz Univ, Fac Sci, Nonlinear Anal & Appl Math NAAM Res Grp, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia

[5] Texas A&M Univ, Dept Math, Kingsville, TX 78363 USA

来源：

MATHEMATICS | 2021年 / 9卷 / 09期

关键词：

Adomian decomposition method; fractional power series method; nonlinear fractional differential equations;

D O I：

10.3390/math9091070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Nonlinear fractional differential equations reflect the true nature of physical and biological models with non-locality and memory effects. This paper considers nonlinear fractional differential equations with unknown analytical solutions. The Adomian decomposition and the fractional power series methods are adopted to approximate the solutions. The two approaches are illustrated and compared by means of four numerical examples.

引用

页数：18

共 31 条

[1] Solution of Singular Integral Equations via Riemann-Liouville Fractional Integrals
Alqudah, Manar A.
Mohammed, Pshtiwan Othman
Abdeljawad, Thabet
[J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2020, 2020
[2] [Anonymous], 2006, Fractional calculus in bioengineering
[3] Fractional Interaction of Financial Agents in a Stock Market Network
Balci, Mehmet Ali
[J]. APPLIED MATHEMATICS AND NONLINEAR SCIENCES, 2020, 5 (01) : 317 - 336
[4] Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method
Bekir, Ahmet
Guner, Ozkan
[J]. CHINESE PHYSICS B, 2013, 22 (11)
[5] CONVERGENCE OF ADOMIAN METHOD
CHERRUAULT, Y
[J]. MATHEMATICAL AND COMPUTER MODELLING, 1990, 14 : 83 - 86
[6] Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method
Duan, Jun-Sheng
Chaolu, Temuer
Rach, Randolph
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (17) : 8370 - 8392
[7] Solution of nonlinear fractional differential equations using homotopy analysis method
Ganjiani, Mehdi
[J]. APPLIED MATHEMATICAL MODELLING, 2010, 34 (06) : 1634 - 1641
[8] A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
Gao, Guang-hua
Sun, Zhi-zhong
Zhang, Hong-wei
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 259 : 33 - 50
[9] A compact finite difference scheme for the fractional sub-diffusion equations
Gao, Guang-hua
Sun, Zhi-zhong
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 230 (03) : 586 - 595
[10] Analytical and approximate solutions of Fractional Partial Differential-Algebraic Equations
Gunerhan, Hatira
Celik, Ercan
[J]. APPLIED MATHEMATICS AND NONLINEAR SCIENCES, 2020, 5 (01) : 109 - 120

← 1 2 3 4 →