Beam bending and Λ-fractional analysis

Abstract

Since the global stability criteria for Λ-fractional mechanics have been established, the Λ-fractional beam bending problem is discussed within that context. The co-existence of the phase phenomenon is revealed, allowing for elastic curves with non-smooth curvatures. The variational bending problem in the Λ-fractional space is considered. Global minimization of the total energy function of beam bending is necessarily applied. The variational Euler-Lagrange equation yields an equilibrium equation of the elastic curve, with the simultaneous possible corners being expressed by Weierstrass-Erdmann corner conditions.

Keywords

• λ-fractional derivative
• λ-fractional space
• initial space
• local stability
• global stability
• coexistence of phases
• elastic curve
• beam bending