Visualization of Fractional Integrals

Abstract

We presented a novel geometric interpretation of the Riemann-Liouville fractional integral. We found that a Riemann-Liouville integral can be thought of as the area obtained by summing together the area of an infinite number of non-rectangular infinitesimals whose shape is determined by the order of integration {\alpha} and the integration limit t. We also showed that this geometric interpretation offers many pedagogical benefits as it is very similar in nature to the geometric interpretation of the Riemann integral.