Abstract
Riemann-Liouville fractional calculus of different orders of 1-dimensional continuous functions is discusses in this paper. Riemann-Liouville fractional integral of 1-dimensional continuous functions of bounded variation of any order still is 1-dimensional continuous functions of bounded variation. Definition of unbounded variation points is given. A 1-dimensional continuous function of unbounded variation based on an unbounded variation point is constructed. We prove that fractal dimension of its Riemann-Liouville fractional integral of any order still is 1. In the end, fractal dimensions of certain 1-dimensional continuous functions of unbounded variation are proved to be 1. Graphs and numerical results of certain example are given.
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