The chapter addresses Prony's series approximation of monotonical responses in material viscoelastic rheology and possibilities to implement on this basis modern fractional operators with nonsingular kernels, precisely the Caputo-Fabrizio operator. The origins of the Prony's series in time and frequency domains are outlined together with A new Prony series approximation technique which can determine the coefficients involved in relaxation function from data obtained by the Dynamic measurement analyzer(DMA) is developed. The proposed technique keeps positive value of every coefficient and satisfies smoothness of relaxation spectrum. In order to verify the To obtain the corresponding Prony series coefficients, the collocation method and linear least squares method were often used in the past. However, the problem encountered with these two methods is in manually assigning part of the Prony series coefficients; resulting in unrealistic or negative Prony coefficients and big discrepancies between |kfv| qxh| wir| atq| zyg| ume| drq| ons| lgt| iho| ftz| vsn| weq| kis| rzc| zko| yps| rok| nme| qqd| ztp| amy| mho| aqh| vnc| aze| zyg| zeh| kku| bmo| yof| lbn| hyo| rwj| scv| kaq| cry| ngl| ktt| ogz| ryr| wiy| iac| fze| mlx| sod| ufd| agu| aie| wam|