Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

被引：137

作者：

Yang, Xiao-Jun ^{[1
,2
]}

Srivastava, H. M. ^{[3
]}

He, Ji-Huan ^{[4
]}

Baleanu, Dumitru ^{[5
,6
,7
]}

机构：

[1] China Univ Min & Technol, Dept Math & Mech, Xuzhou 221008, Jiangsu, Peoples R China

[2] Qujing Normal Univ, Inst Appl Math, Qujing 655011, Peoples R China

[3] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[4] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, Suzhou 215123, Peoples R China

[5] Cankaya Univ, Fac Arts & Sci, Dept Math & Comp Sci, TR-06530 Ankara, Turkey

[6] King Abdulaziz Univ, Dept Chem & Mat Engn, Fac Engn, Jeddah 21589, Saudi Arabia

[7] Inst Space Sci, Magurele, Romania

来源：

PHYSICS LETTERS A | 2013年 / 377卷 / 28-30期

关键词：

Heat-conduction equation; Damped wave equation; Local fractional derivatives; Cantor set; NAVIER-STOKES EQUATION; COMPLEX TRANSFORM; CALCULUS; MECHANICS;

D O I：

10.1016/j.physleta.2013.04.012

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems. (c) 2013 Published by Elsevier B.V.

引用

页码：1696 / 1700

页数：5

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