Journal of Statistics Applications & Probability

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The functional variational principle and differential equations of motion for the Lee–Wick electrodynamics equation are investigated in this study. A functional Hamiltonian principle is built utilizing the concept of a functional derivative. The Hamiltonian formulation of third-order continuous field systems is created using functional derivatives for continuous third-order systems. The formalism is generalized, and this new formulation is used to solve the Lee–Wick electrodynamics equation. We used the Euler-Lagrange equations for these systems to compare the results obtained using Hamiltons equations in terms of functional derivatives. To compare the outcomes of the two methodologies in terms of functional derivatives, one example has been presented. The results of this study show that functional calculus has more flexible models than classical calculus due to the ordering of the functional derivative and the functional operator. This property is critical when developing a novel generalization of the Lee-Wick equation using functional derivatives.

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