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We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters.

This paper is concerned with the stability of traveling wave fronts for a coupled system of non-local delayed lattice differential equations with a quiescent stage. It shows that under certain conditions all non-critical traveling wave fronts are globally exponentially stable, and critical ftraveling wave fronts are globally algebraically stable by applying the weighted energy method and the semi-discrete Fourier transform. [ABSTRACT FROM AUTHOR]