As is evident from the preceding discussion, there is a dearth of research on the reaction of beams on fractional derivative foundations, with the majority of investigations concentrating on finite beams and only a few limited inquiries exploring the response of infinite beams. Additionally, the majority of these studies have neglected to consider the impact of lateral forces between soils. To remedy this, the present study employs a fractional viscoelastic Pasternak model to emulate the foundation and explores the dynamic response of an Euler beam subjected to a moving load, as well as the influence of the order of fractional derivatives and different foundation beam parameters on the vibration response.


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