On the Connection Between the Order of Riemann-Liouville Fractional Calculus and Hausdorff Dimension of a Fractal Function

Abstract

This paper investigates the fractal dimension of the fractional integrals of a fractal function. It has been proved that there exists some linear connection between the order of Riemann-Liouville fractional integrals and the Hausdorff dimension of a fractal function.