On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Abstract

In the process of constructing empirical mathematical models of physical phenomena using the fractional calculus, investigators are usually faced with the choice of which definition of the fractional derivative to use, the Riemann-Liouville definition or the Caputo definition. This investigation presents the case that, with some minimal restrictions, the two definitions produce completely equivalent mathematical models of the linear viscoelastic phenomenon.