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CONNECTION BETWEEN THE ORDER OF FRACTIONAL CALCULUS AND FRACTIONAL DIMENSIONS OF A TYPE OF FRACTAL FUNCTIONS 被引量：7

CONNECTION BETWEEN THE ORDER OF FRACTIONAL CALCULUS AND FRACTIONAL DIMENSIONS OF A TYPE OF FRACTAL FUNCTIONS
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摘要 The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship. The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
作者 Yongshun Liang Weiyi Su
机构地区 Nanjing University of Science and Technology Nanjing University
出处 《Analysis in Theory and Applications》 2007年第4期354-362,共9页 分析理论与应用（英文刊）
基金 NSFC,grant 10171045,10571084.
关键词 generalized Weierstrass function Riemann-Liouville fractional calculus fractal dimension LINEAR GRAPH generalized Weierstrass function, Riemann-Liouville fractional calculus, fractal dimension, linear, graph
分类号 O17 [理学—基础数学]
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参考文献10

  • 1Falconer,J.Fractal Geometry:Mathematical Foundations and Applications[]..1990
  • 2Hu,T.Y,and Lau,K.S.Fractal Dimensions and Singularities of the Weierstrass Type Functions[].Transactions of the American Mathematical Society.1993
  • 3Mandelbrot,B.B.The Fractal Geometry of Naturem[]..1977
  • 4Kolwankar,K.M,and Gangal,A.D.Fractional Differentiability of Nowhere Differentiable Functions and Dimensions[].Chaos.1996
  • 5Ross,B.Fractional Calculus and its Applications[]..1975
  • 6Wen,Z.Y.Mathematical Foundations of Fractal Geometry[]..2000
  • 7Yao,K,Su,W.Y,and Zhou,S.P.On the Fractional Calculus of a Type of Weierstrass Function[].Chinese Annals of Mathematics.2004
  • 8Liang,Y.S,and Su,W.Y.The Relationship Between the Fractal Dimensions of a Type of Fractal Functions and the Order of Their Fractional Calculus[].Chaos Solitons Fractals.2007
  • 9Liang,Y.S,and Yao,K.The Fractal Dimensions of Graphs of the Weyl-Marchaud Fractional Derivative of the Weierstrass Function[].International Journal of Nonlinear Sciences and Numerical Simulation.
  • 10Yao,K,and Liang,Y.S.The Fractal Dimensions of the Weyl-Marchaud Fractional Derviative of the Weierstrass-type Function[].Chaos Solitons Fractals.

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Analysis in Theory and Applications
2007年 第4期

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