Deflection of Beams Modeled by Fractional Differential Equations

Abstract

Using the concept of a fractional derivative, in Caputo’s sense, we derive and solve a fractional differential equation that models the deflection of beams. The scheme to introduce the fractional concept can be used for different situations; in the article, we only consider four cases as an example of its usefulness. In addition, we establish a relationship between the fractional index and the level of stiffness (or flexibility) of the material with which the beam is made.