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The main aim of this paper is to discuss the electrodynamics of relativistic dynamics of particles bases on the notion of the non-standard Lagrangians which have gained increasing importance in the theory of nonlinear differential equations, dissipative dynamical systems and theoretical physics. The mathematical settings are constructed starting from the modified Euler-Lagrange equation and modified Hamiltons equations. Some illustrative examples are considered and discussed.
}, issn = {2079-7346}, doi = {https://doi.org/10.4208/jams.040214.061414a}, url = {http://global-sci.org/intro/article_detail/jams/8313.html} }The main aim of this paper is to discuss the electrodynamics of relativistic dynamics of particles bases on the notion of the non-standard Lagrangians which have gained increasing importance in the theory of nonlinear differential equations, dissipative dynamical systems and theoretical physics. The mathematical settings are constructed starting from the modified Euler-Lagrange equation and modified Hamiltons equations. Some illustrative examples are considered and discussed.