参考文献 [1] Liang Y. S., The relationship between the Box dimension of the Besicovitch functions and the orders of their fractional calculus, Applied Mathematics and Computation, 2008, 200: 197-207.
[2] Tatom F. B., The relationship between fractional calculus and fractals, Fractals, 1995, 3(1): 217-229.
[3] Yao K., Su W. Y., Zhou S. P., On the fractional derivatives of a fractal function, Acta Mathematica Sinica, English Series, 2006, 22(3): 719-722.
[4] Z¨ahle M., Ziezold H., Fractional derivatives of Weierstrass-type functions, J. Computational and Appl. Math., 1996, 76: 265-275.
[5] Oldham K. B., Spanier J., The Fractional Calculus, New York: Academic Press, 1974.
[6] Liang Y. S., Su W. Y., The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus, Chaos, Solitons and Fractals, 2007, 34: 682-692.
[7] Liang Y. S., Connection between the order of fractional calculus and fractional dimensins of a type of fractal functions, Analysis Theory and its Application, 2007, 23: 354-363.
[8] Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equation, New York: John Wiley. Sons. Inc., 1993.
[9] Falconer J., Fractal Geometry: Mathematical Foundations and Applications, New York: John Wiley Sons Inc., 1990.
[10] Hu T. Y., Lau K. S., Fractal dimensions and singularities of the Weierstrass type functions, Trans. Amer. Math. Soc., 1993, 335(2): 649-665.
|