Modified fractional Euler method for solving Fuzzy Fractional Initial Value Problem

被引：186

作者：

Mazandarani, Mehran ^{[1
]}

Kamyad, Ali Vahidian ^{[2
]}

机构：

[1] Ferdowsi Univ Mashhad, Dept Elect Engn, Mashhad, Iran

[2] Ferdowsi Univ Mashhad, Dept Appl Math, CEMCS, Mashhad, Iran

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2013年 / 18卷 / 01期

关键词：

Fuzzy Fractional Differential Equations; Fractional Initial Value Problem; Caputo-type fuzzy fractional derivative; Fractional Euler method; DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.cnsns.2012.06.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the solution to Fuzzy Fractional Initial Value Problem [FFIVP] under Caputotype fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylor's formula and a modified trapezoidal rule is used for solving initial value problem under fuzzy fractional differential equation of order beta subset of (0, 1). Solving two examples of linear and nonlinear FFIVP illustrates the method. (c) 2012 Elsevier B.V. All rights reserved.

引用

页码：12 / 21

页数：10

共 15 条

[1]

Anastassiou George A., 2011, MATHEMATICS, P553

[2]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[3]

Arshad S, 2011, ELECTRON J QUAL THEO, P1

[4] On the fractional differential equations with uncertainty [J].

Arshad, Sadia ;

Lupulescu, Vasile .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (11) :3685-3693

[5] Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations [J].

Bede, B ;

Gal, SG .

FUZZY SETS AND SYSTEMS, 2005, 151 (03) :581-599

[6]

Dumitru Baleanu, 2011, FRACT DYNAM CONTROL

[7] Homotopy analysis method for fractional IVPs [J].

Hashim, I. ;

Abdulaziz, O. ;

Momani, S. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (03) :674-684

[8] Fractional calculus in viscoelasticity: An experimental study [J].

Meral, F. C. ;

Royston, T. J. ;

Magin, R. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (04) :939-945

[9]

Odibat Zaid M., 2008, Journal of Applied Mathematics and Informatics, V26, P15

[10]

ODIBAT ZM, 2007, J APPL MATH COMPUT, V186, P286, DOI DOI 10.1016/J.AMC.2006.07.102

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