Analyzing Riemann-Liouville constraints in second-order Lagrangian fractional electrodynamic models

Abstract

This study used second-order fractional derivatives to constrain singular Lagrangians to construct comprehensive Hamilton-Dirac equations. Notable contributions include resolving the difficulties associated with fractional derivatives. This modeling methodology efficiently covers non-local and non-differentiable fractional derivatives, giving a systematic strategy for dealing with modeling complexity. It establishes fractional equations that connect Coulomb’s law to the principle of superposition. Furthermore, we extended the Hamilton-Jacobi formalism by incorporating second-order derivatives in the context of Podolsky’s electrodynamics. This approach provides a solution for overcoming limitations in singular Lagrangians by linking the principles of Lagrangian fractional electrodynamics and classical field theory. The novelty of this work lies in its methodological approach to resolving the challenges of second-order fractional derivatives, particularly with respect to non-locality and memory effects, which have not been adequately addressed in previous models. This research offers new insights into expanding classical field theory using fractional calculus, opening new avenues for understanding interactions in electrodynamic systems. The results suggest that fractional formulations broaden the boundaries of traditional theories, providing a framework that encompasses a wider range of dynamic behaviors and advancing the understanding of fractional electrodynamics beyond previous studies. Furthermore, this approach paves the way for future research into fractional special relativity theories.