One has recently presented an extension of the standard variational calculus to include the presence of deformed derivatives, both in the Lagrangian of systems of particles and in the Lagrangian density of field-theoretic models. Classical Euler-Lagrange equations and the Hamiltonian formalism have been reassessed in this approach. Whenever applied to a number of physical systems, the resulting dynamical equations come out to be the correct ones found in the literature, especially with mass-dependent and with nonlinear equations for classical and quantum-mechanical systems. In the present contribution, one extends the variational approach, including a piecewise form of deformed derivatives to study higher-order dissipative systems and to obtain, as an option, deformed equations as well. Applications to concrete situations are contemplated, such as an accelerated point charge—this is the problem of the Abraham-Lorentz-Dirac force—stochastic dynamics like the Langevin, the advection-convection-reaction and Fokker-Planck equations, the Korteweg-de Vries equation, the Landau-Lifshitz-Gilbert problem, and the Caldirola-Kanai Hamiltonian and heat transfer equation of the Fourier and non-Fourier types. By considering these different examples, it is shown that the formulation proposed in this paper may be a simple, but promising, path for dealing, for example, with dissipative, nonlinear, stochastic systems and the anomalous heat transfer problem, by adopting a variational approach.