A NOTE ON FRACTAL DIMENSION OF RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL

This paper intends to study the analytical properties of the Riemann-Liouville fractional integral and fractal dimensions of its graph on Double-struck capital R-n. We show that the Riemann-Liouville fractional integral preserves some analytical properties such as boundedness, continuity and bounded variation in the Arzela sense. We also deduce the upper bound of the box dimension and the Hausdorff dimension of the graph of the Riemann-Liouville fractional integral of Holder continuous functions. Furthermore, we prove that the box dimension and the Hausdorff dimension of the graph of the Riemann-Liouville fractional integral of a function, which is continuous and of bounded variation in Arzela sense, are n.