Integrals and derivatives on net fractals

被引：57

作者：

Ren, FY ^{[1
]}

Liang, JR

Wang, XT

Qiu, WY

机构：

[1] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China

[2] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2003年 / 16卷 / 01期

关键词：

D O I：

10.1016/S0960-0779(02)00211-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper a framework of calculus on net fractals is built. Integrals and derivatives of functions in net measure are discussed. Approximate calculations of the integrals and derivatives and approximate solutions to the inverse problem of integrals in net measure are given. In addition, applications of the calculus in some physical systems, such as in diffusion processes and in memory processes are given. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：107 / 117

页数：11

共 16 条

[1]

[Anonymous], 1992, TEORETICHESKAYA MATE, DOI [DOI 10.1007/BF01036529, 10.1007/BF01036529]

[2]

BEDFORD T, 1989, NAIO ASI SERIES

[3]

Falconer K., 1997, Techniques in fractal geometry

[4]

Falconer K., 1990, FRACTAL GEOMETRY MAT, V2

[5] FRACTIONAL DIFFUSION EQUATION FOR TRANSPORT PHENOMENA IN RANDOM-MEDIA [J].

GIONA, M ;

ROMAN, HE .

PHYSICA A, 1992, 185 (1-4) :87-97

[6] FRACTALS AND SELF SIMILARITY [J].

HUTCHINSON, JE .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) :713-747

[7]

Kilbas AA, 1993, Fractional Integral and Derivatives: Theory and Applications

[8]

NIGMATULLIN RR, UNPUB TIME ARROW FRA

[9] Fractional integrals and fractal structure of memory sets [J].

Qiu, WY ;

Lü, J .

PHYSICS LETTERS A, 2000, 272 (5-6) :353-358

[10] Fractional integral associated to the self-similar set or the generalized self-similar set and its physical interpretation [J].

Ren, FY ;

Yu, ZG ;

Su, F .

PHYSICS LETTERS A, 1996, 219 (1-2) :59-68

← 1 2 →