Construction For A Class Of Particular Fractal Functions

In just a few decades,the development of fractal theory is increasingly deepening,the applied range of fractal is increasingly wide.The unique charm of fractal has at-tracted attention of more and more scholars,which makes analysis of fractal sets and functions with more vigor.The construction of fractal functions is an important subject in fractal research.Fractal functions with special structure have a great significance on the structural analysis of fractal functions and fractal dimension of fractal functions.This article focuses on the construction and property of special fractal functions,and studies the relationship between fractal dimension of fractional calculus of fractal func-tions and fractal dimension of fractal functions by fractional calculus.In this paper,we first construct a one-dimensional continuous fractal function,and discuss the number of unbounded variation points.It's proved that fractal dimension of its Riemann-Liouville fractional integral is 1.Then,on the basis of Von Koch curve,fractal functions with uncountable unbounded variation points are constructed.The length of graphs of these functios are calculated to be3n/4n and it's proved that their fractal dimension is log3 4.In the end,a class of fractal functions without expressions has been studied.Upper bound estimation of upper Box dimension of Riemann-Liouville fractional integral of order v of any continuous functions on a closed interval has been proved to be no more than 2-v when 0 ? v ? 1.If a continuous function which satisfies ?-Ho1der condition on a closed interval,upper Box dimension of its Riemann-Liouville fractional integral is no more than 2-? when 0 ? a ? 1.