Generalized Hamilton's Principle with Fractional Derivatives

TL;DR

This paper extends Hamilton's principle by incorporating fractional derivatives into the Lagrangian, allowing variation in both the function and the derivative order, leading to new stationarity conditions.

Contribution

It introduces a generalized variational framework with fractional derivatives, varying both the function and derivative order, and derives corresponding stationarity conditions.

Findings

Derived new stationarity conditions for fractional variational problems.

Demonstrated the framework through several illustrative examples.

Abstract

We generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t),\alpha)$ so that the function $y$ and the order of fractional derivative $\alpha$ are varied in the minimization procedure. We derive stationarity conditions and discuss them through several examples.