Hamiltonian Formulation of Classical Fields with Fractional Derivatives

TL;DR

This paper develops a fractional Hamiltonian framework for classical fields, deriving Hamilton's equations with fractional derivatives, and demonstrates the approach with two example fields, showing similarities to traditional classical field theory.

Contribution

It introduces a fractional Hamiltonian formulation for classical fields, extending classical theory with fractional derivatives and deriving corresponding Hamilton's equations.

Findings

Derived fractional Hamilton's equations for classical fields.

Showed the formulation's similarity to classical field theory.

Presented two example applications of the fractional approach.

Abstract

An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the resulting equations are very similar to those appearing in classical field theory.