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New aspects on the fractional Euler-Lagrange equation with non-singular kernels

Rangaig Norodin A.

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 4

89--100

In this paper, we presented some notes in utilizing the fractional integral counterparts of the fractional derivatives with non-singular kernels on the action-like integral in Lagrangian mechanics. Considering a fractional integral, it may suggest that a dissipative term on the resulting fractional Euler-Lagrange equation can be obtained due to the imposed kernel. However, in the case of nonsingular kernel operators, different aspects of the fractional action-like integral were observed, and corresponding (fractionally-modified) Euler-Lagrange were derived, which imposes new insights on the dynamical system under the fractional regime.