Hamilton formulation for generalized Proca electrodynamics using fractional derivative

Abstract

We use fractional derivatives to reformulate the Proca equation in this study. The Riemann–Liouville fractional derivative operator is defined, and a fractional variational principle based on this definition is constructed. The formalism is generalized, and this new formulation is used in the Proca electrodynamics equation. Fractional derivatives are used to derive both the fractional Euler equations and the fractional Hamilton equations. Furthermore, we found that fractional Euler-Lagrange and fractional Hamiltonian equations yield the same result. Finally, we studied one specific example to demonstrate the findings.