Fractional differential operators and generalized oscillatory dynamics. (English) Zbl 1484.26005
Summary: In this paper, a new generalized fractional derivative is introduced holding many important properties. By implementing this new definition inside the Lagrangian \(L: \mathcal{TQ}\to \mathbb{R}\), where \(\mathcal{Q}\) is an \(n\)-dimensional manifold and \(\mathcal{TQ}\) its tangent bundle, the new definition was used to discuss many interesting and general properties of the Lagrangian and Hamiltonian formalisms starting from a fractional actionlike variational approach. Applications of the new formalism for solving some dynamical oscillatory models of fractional order are given. Additional attractive features are explored in some details.
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