Mechanics with non-Leibniz derivatives

The non-Leibniz Hamiltonian and Lagrangian formalism for the certain class of dissipative systems is introduced in this article.The formalism is based on the generalized differentiation operator with a non-zero Leibniz defect.The Leibniz defect of the introduced operator linearly depends on one scaling parameter.In a special case, if the Leibniz defect vanishes, the -operator reduces to the common differentiation operator.The new operator allows the formulation of the variational principles and corresponding equations of Lagrange and Hamiltonian types for dissipative systems.The solutions of some generalized dynamical equations are provided in closed form.