Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

TL;DR

This paper introduces a fractional calculus framework for dynamical systems, deriving fractional Hamilton and Euler-Lagrange equations, and formulating fractional equations of motion based on fractional variations of classical Lagrangians and Hamiltonians.

Contribution

It presents a novel fractional calculus approach to classical mechanics, extending Hamilton and Lagrange formalisms with fractional derivatives and equations of motion.

Findings

Derived fractional Hamilton and Euler-Lagrange equations.

Formulated fractional equations of motion from fractional variations.

Extended classical mechanics with fractional calculus methods.

Abstract

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.