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Riemann-Liouville fractional calculus of Blancmange Curve and Cantor Functions are studied in this paper. In this paper, Blancmange Curve and Cantor function defined on the interval is shown to be Fractal Interpolation Functions with appropriate interpolation points and parameters. Then, using the properties of Fractal Interpolation Function, the Riemann-Liouville fractional integral of Blancmange Curve and Cantor function are described to be Fractal Interpolation Function passing through a different set of points. Finally, using the conditions for the fractional derivative of order ν of a FIF, it is shown that the fractional derivative of Blancmange Curve and Cantor function is not a FIF for any value of ν.

Riemann-Liouville Fractional Calculus of Blancmange Curve and Cantor Functions