The standard integer order differential equation can’t be used to describe the memory mechanics behavior and the power-law frequency-denpendent damping of the viscoelastic materials,so the fractal derivative,the fractional derivative and the positive fractional derivative is employed to depict the damped oscillation in the viscoelastic medium.

In the present paper, the fractional derivative model in Riemann-Liouville form is adopted to describe the viscous property of the matrix.

In the present paper a new concept of "fractional derivative" is adopted to describe the viscoelastic property of the plastic matrix.

The viscoelasticities of various polymers have been fitted with viscoelastic fractional derivative models.

This work is devoted to investigating exact solutions of generalized fractional diffusion equation in the boundary condition and the general initial condition with the Laplace transform method by introducing the concept of Riemann-Liouville fractional derivative,then change initial condition,study the first passage time distribution problem,and validate the exact solutions exist.

Analytical approach of waveform attribute based on fractional order derivative;

Application of fractional order derivative in analyzing seismic singularity

The aim of this paper is to give a simulation of creep and relaxation laws of concrete with aging by using standard-linear-like body with fractional order derivatives.

The derivatives of fractional order of this function are foundout in this paper.

Experiments show that fractional-order derivative model is more precise than integer-order derivative model of the transfer function,and the nonlinear characteristics of the damping system are related to the fractional orders.