The fuzzy generalized Taylor's expansion with application in fractional differential equations

被引：0

作者：

Armand, A. ^{[1
]}

Allahviranloo, T. ^{[1
]}

Abbasbandy, S. ^{[1
]}

Gouyandeh, Z. ^{[2
]}

机构：

[1] Islamic Azad Univ, Dept Math, Sci & Res Branch, Tehran, Iran

[2] Islamic Azad Univ, Najafabad Branch, Dept Math, Najafabad, Isfahan, Iran

来源：

IRANIAN JOURNAL OF FUZZY SYSTEMS | 2019年 / 16卷 / 02期

关键词：

Generalized Hukuhara derivative; Caputo generalized Hukuhara derivative; Fuzzy mean value theorem for Riemann-Liouville integral; Generalized Taylor's expansion; Fuzzy fractional differential equations; Fuzzy fractional Euler's method; VALUED FUNCTIONS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the generalized Taylor's expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzy fractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessary that we prove them in details. In application, the fractional Euler's method is derived for solving fuzzy fractional differential equations in the sense of Caputo differentiability. The effectiveness of the proposed method is verified by three examples.

引用

页码：57 / 72

页数：16

共 30 条

[1] On the concept of solution for fractional differential equations with uncertainty [J].

Agarwal, Ravi P. ;

Lakshmikantham, V. ;

Nieto, Juan J. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :2859-2862

[2] A Jacobi operational matrix for solving a fuzzy linear fractional differential equation [J].

Ahmadian, Ali ;

Suleiman, Mohamed ;

Salahshour, Soheil ;

Baleanu, Dumitru .

ADVANCES IN DIFFERENCE EQUATIONS, 2013,

[3] Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations [J].

Alikhani, Robab ;

Bahrami, Fariba .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2013, 18 (08) :2007-2017

[4] Fuzzy fractional differential equations under generalized fuzzy Caputo derivative [J].

Allahviranloo, T. ;

Armand, A. ;

Gouyandeh, Z. .

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2014, 26 (03) :1481-1490

[5] Explicit solutions of fractional differential equations with uncertainty [J].

Allahviranloo, T. ;

Salahshour, S. ;

Abbasbandy, S. .

SOFT COMPUTING, 2012, 16 (02) :297-302

[6]

Allahviranloo T., 2013, J. Fuzzy Set Valued Anal, V2013, P00163

[7] On fuzzy solutions for heat equation based on generalized Hukuhara differentiability [J].

Allahviranloo, Tofigh ;

Gouyandeh, Zienab ;

Armand, Atefeh ;

Hasanoglu, Alemdar .

FUZZY SETS AND SYSTEMS, 2015, 265 :1-23

[8]

Anastassiou G. A., 2010, STUDIES FUZZINESS SO, V251, P1434

[9]

[Anonymous], 2012, ADV DIFFER EQU

[10]

Armand A, 2016, J APPL ANAL COMPUT, V6, P119

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