Speaker
Description
Fractional calculus is a powerful extension of the traditional calculus, which found its way to modeling complex phenomena such as anomalous diffusion, heat conduction, elasticity and plasticity, or micro/nano beams. The wide spectrum of applications of this branch of mathematical analysis is related to its nonlocal nature, which allows to describe problems where it is necessary to take into account the influence of the surrounding of a point in a given space, while analyzing the behavior of the phenomenon there. Since in many cases the affecting neighborhood is not only one-sided, special both-sided operators, such as compositions of fractional derivatives, have been gaining popularity.
In our work we consider the fractional Euler - Bernoulli beam equation including the composition of the left and right Caputo derivatives. We analyze two types of boundary conditions: beam with fixed-supported and fixed-free ends and employ numerical methods, based on the trapezoidal rule, to obtain the approximated solutions of the given equation. We perform the numerical simulations for three particular downward transverse loads per unit length: constant, power and trigonometric function. Additionally, for each case, we conduct an analysis of orders of accuracy of the proposed method.
