A remark on the fractional order differential equations

被引：5

作者：

Zhang, Tie ^{[1
]}

Tong, Can ^{[1
]}

机构：

[1] Northeastern Univ, Dept Math, Shenyang 110004, Liaoning, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 340卷

关键词：

Fractional differential equation; Solving method; Counter-example; SLIDING-MODE OBSERVER; CHAOTIC SYSTEMS; SYNCHRONIZATION; STABILITY; ALGORITHM;

D O I：

10.1016/j.cam.2018.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An important solving method was presented in article (Demirci and Ozalp, 2012) which shows that: "The exact solution of a fractional order differential equation can be obtained by means of the solution of an integer order differential equation". This article and its method have been cited by many researchers. In this paper, we will show that this solving method is wrong, and then we use several counter-examples to disconfirm this solving method. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：375 / 379

页数：5

共 20 条

[1] Super-Twisting Algorithm-Based Sliding-Mode Observer for Synchronization of Nonlinear Incommensurate Fractional-Order Chaotic Systems Subject to Unknown Inputs [J].

Al-Saggaf, Ubaid Muhsen ;

Bettayeb, Maamar ;

Djennoune, Said .

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 2017, 42 (07) :3065-3075

[2]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[3]

Demirci E., 2017, ADV DIFFERENTIAL EQU, V79, P1

[4] A method for solving differential equations of fractional order [J].

Demirci, Elif ;

Ozalp, Nuri .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (11) :2754-2762

[5] Observation and sliding mode observer for nonlinear fractional-order system with unknown input [J].

Djeghali, Nadia ;

Djennoune, Said ;

Bettayeb, Maamar ;

Ghanes, Malek ;

Barbot, Jean-Pierre .

ISA TRANSACTIONS, 2016, 63 :1-10

[6] Waveform relaxation methods for fractional differential equations with the Caputo derivatives [J].

Jiang, Yao-Lin ;

Ding, Xiao-Li .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 238 :51-67

[7] A method for solving differential equations of q-fractional order [J].

Koca, Ilknur .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 266 :1-5

[8]

Lakshmikantham V., 2007, Commun. Appl. Anal, V11, P395

[9] Observer-based robust stabilisation of a class of non-linear fractional-order uncertain systems: an linear matrix inequalitie approach [J].

Li, C. ;

Wang, J. ;

Lu, J. .

IET CONTROL THEORY AND APPLICATIONS, 2012, 6 (18) :2757-2764

[10]

Li YT, 2014, NONLINEAR DYNAM, V78, P2909, DOI 10.1007/s11071-014-1635-3

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