Local Fractional Newton's Method Derived from Modified Local Fractional Calculus

被引:5
作者
Gao, Feng [1 ]
Yang, Xiaojun [1 ]
Kang, Zongxin [1 ]
机构
[1] China Univ Min & Technol, Coll Sci, Xuzhou 221008, Jiangsu, Peoples R China
来源
INTERNATIONAL JOINT CONFERENCE ON COMPUTATIONAL SCIENCES AND OPTIMIZATION, VOL 1, PROCEEDINGS | 2009年
关键词
BROWNIAN-MOTION; MECHANICS; EQUATION; ORDER; DIFFERENTIABILITY; DERIVATIVES;
D O I
10.1109/CSO.2009.330
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
A local fractional Newton's method, which is derived from the modified local fractional calculus, is proposed in the present paper. Its iterative function is obtained and the convergence of the iterative function is discussed. The comparison between the classical Newton iteration and the local fractional Newton iteration has been carried out. It is shown that the iterative value of the local fractional Newton method better approximates the real-value than that of the classical one.
引用
收藏
页码:228 / 232
页数:5
相关论文
共 16 条
[1]  
Adda Faycal Ben., 2001, Journal of Mathematical Analysis and Applications, V263, P721, DOI [10.1016/ j. jmaa. 2013.06.027, DOI 10.1006/JMAA.2001.7656]
[2]   On calculus of local fractional derivatives [J].
Babakhani, A ;
Daftardar-Gejji, V .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 270 (01) :66-79
[3]  
BARTELS R, 1993, INTRO NUMERICAL ANAL
[4]   Fractional order continuity and some properties about integrability and differentiability of real functions [J].
Bonilla, B ;
Trujillo, JJ .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 231 (01) :205-212
[5]   A fractal theory for the mechanics of elastic materials [J].
Carpinteri, A ;
Chiaia, B ;
Cornetti, P .
MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING, 2004, 365 (1-2) :235-240
[6]   Calculation of the tensile and flexural strength of disordered materials using fractional calculus [J].
Carpinteri, A ;
Cornetti, P ;
Kolwankar, KM .
CHAOS SOLITONS & FRACTALS, 2004, 21 (03) :623-632
[7]   Static-kinematic duality and the principle of virtual work in the mechanics of fractal media [J].
Carpinteri, A ;
Chiaia, B ;
Cornetti, P .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 191 (1-2) :3-19
[8]   On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion [J].
Jumarie, G .
APPLIED MATHEMATICS LETTERS, 2005, 18 (07) :817-826
[9]   On the representation of fractional Brownian motion as an integral with respect to (dt)a [J].
Jumarie, G .
APPLIED MATHEMATICS LETTERS, 2005, 18 (07) :739-748
[10]   Fractional master equation: non-standard analysis and Liouville-Riemann derivative [J].
Jumarie, G .
CHAOS SOLITONS & FRACTALS, 2001, 12 (13) :2577-2587