Abstract
A one-dimensional continuous function of unbounded variation on [0, 1] has been constructed. The length of its graph is infinite, while part of this function displays fractal features. The Box dimension of its Riemann-Liouville fractional integral has been calculated.
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Supported by National Natural Science Foundation of China and Natural Science Foundation of Jiangsu Province (Grant Nos. 11201230 and BK2012398)
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Zhang, Q. Some remarks on one-dimensional functions and their Riemann-Liouville fractional calculus. Acta. Math. Sin.-English Ser. 30, 517–524 (2014). https://doi.org/10.1007/s10114-013-2044-0
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DOI: https://doi.org/10.1007/s10114-013-2044-0