Speaker
Description
Fractional calculus is gaining increasing recognition among scientists from various fields of science, and one of its key applications is continuum mechanics. The introduction of nonlocality to models of this field has enabled the development of a fractional theory of continuum mechanics, which opens up new perspectives in modeling and analyzing the behavior of materials and structures. The newly created models contain fractional operators with a fixed memory length, which poses a problem in determining their solutions. Existing analytical solutions include only selected types of equations, which emphasizes the need to develop numerical and approximate methods that allow for the effective application of this theory in practice. In our work, we discuss the numerical approximation of fractional compositions of Caputo derivatives with fixed memory length. We also present the application of this type of operator to modeling a one-dimensional problem of continuous mechanics. The composition of fractional operators is approximated by the trapezoidal rule. The obtained numerical solution is compared with approximate solutions for selected functions. Then, we use the derived numerical scheme to determine the solution of beam displacement under given Dirichlet boundary conditions.
