ANALYTICAL AND NUMERICAL SOLUTION OF THE FRACTIONAL EULER-BERNOULLI BEAM EQUATION

摘要

In this paper a new formulation of the Euler-Bernoulli beam equation is proposed, which is based on fractional calculus. The fractional Euler-Bernoulli beam equation is derived by using a variational approach. Such formulation leads to an equation containing left and right fractional Caputo derivatives simultaneously. The obtained equation is transformed into an integral equation and then is solved analytically and numerically. Finally, examples of computations and error analysis are shown.