| 摘 要： | 1 IntroductionIn recent years, fractals have shown important applications in many fields. [1,2] and [3] have done some excellent initial and conclusion work on fractal and it's mathematical foundations. However, a fractal function: a type of Weierstrass functions defined byW(t) = (?), 0 < a < 1, A > 1, (1)because of it's special fractal properties, [1, 2, 4, 5] have given some detailed discussion about it's graph, fractal dimension, etc.Fractional calculus attract more and more attention recently. In this field, [6, 7] have done some important and detailed work. The fundamental conception is
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