Fractional Differential Operators and Generalized Oscillatory Dynamics

Rami Ahmad El-Nabulsi

Abstract

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.