Abstract

In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional nonlinear dynamic equations involving the classical physical application "Spring-Mass-Dumper System" to both, integer order calculus (IOC) and fractional order calculus (FOC) approaches. After the numerical simulations, we outlined the main results through time histories and the investigation of phase portraits. Thereafter, we believe that the results showed on this paper are pertinent enough to be thoroughly analyzed and maybe it can be the very beginning of a stride towards more realistic and more precise results about fractional-order models when compared to the integer order models in these applications.

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