An Application of Fractional Calculus to Column Theory

TL;DR

This paper introduces a fractional calculus approach to column buckling, deriving a fractional differential equation and identifying critical buckling forces for specific fractional parameters, supported by a numerical approximation scheme.

Contribution

It applies fractional calculus to classical column theory, deriving a new fractional differential equation and providing a numerical method to estimate critical buckling forces.

Findings

Existence of critical buckling force for certain fractional parameters

Derivation of a fractional differential equation in Caputo sense

Development of a numerical scheme for force approximation

Abstract

In this article, we employ a fractional version of the radius of curvature in Euler's equation for column buckling, enabling us to derive a fractional differential equation in the Caputo sense. We solve this equation and demonstrate that for certain values of the fractional parameter, there exists a critical buckling force. Additionally, we provide a numerical scheme for accurately approximating this critical force.