Abstract
Fractional integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville fractional integral is v, fractal dimension of Riemann-Liouville fractional integral of any continuous functions on a closed interval is no more than 2 - v.
Highlights
In [1], fractional integral of a continuous function of bounded variation on a closed interval has been proved to still be a continuous function of bounded variation
The upper bound of Box dimension of the Weyl-Marchaud fractional derivative of self-affine curves has given in [2]
If U is any non-empty subset of n-dimensional Euclidean space, Rn, the diameter of U is defined as
Summary
In [1], fractional integral of a continuous function of bounded variation on a closed interval has been proved to still be a continuous function of bounded variation. The upper bound of Box dimension of the Weyl-Marchaud fractional derivative of self-affine curves has given in [2]. Previous discussion about fractal dimensions of fractional calculus of certain special functions can be found in [3] [4]. We discuss fractional integral of fractal dimension of any continuous functions on a closed interval.
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