Fractional Operator Viscoelastic Models in Dynamic Problems of Mechanics of Solids: A Review
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Title
Fractional Operator Viscoelastic Models in Dynamic Problems of Mechanics of Solids: A Review
Authors
Keywords
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Journal
Mechanics of Solids
Volume -, Issue -, Pages -
Publisher
Allerton Press
Online
2021-12-08
DOI
10.3103/s0025654422010022
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- (2021) Sergei Rogosin et al. Fractional Calculus and Applied Analysis
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- (2008) Yury A. Rossikhin et al. MECHANICS OF TIME-DEPENDENT MATERIALS
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