2018/03/09 by Roberto Garra, Garra, Roberto, Francesco Mainardi +1
Chemical Engineering · Engineering · Mathematics · Physics and Astronomy · #26A33 #33E12 #74D05 #76A05 #FOS: Physical sciences #Fractional Differential Equations Solutions #Numerical methods in engineering #Rheology and Fluid Dynamics Studies #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft #msc:26A33 #msc:33E12 #msc:74D05 #msc:76A05
paper · pdf · doi:10.48550/arxiv.1803.03408
6 pages. I withdraw because with other two researechers (Giusti and Colombaro) have appointed a more detailed version (Garra and Mainardi)
openalex publication_date 2018/03/09 · openalex created_date 2018/03/29 · arxiv created 2018/08/17 · arxiv updated 2018/08/20 · openalex updated_date 2026/07/28
In a recent paper, Zhou et al. studied the time-dependent properties of Glass Fiber Reinforced Polymers (GFRP) composites by using a new rheological model with a time-variable viscosity coefficient. This rheology is essentially based on a generalized Scott-Blair model with time-varying viscosity coefficient involving Riemann-Liouville fractional derivatives. Motivated by this study, in this note we suggest a different generalization of the Scott-Blair model based on the application of Caputo fractional derivatives of a function with respect to another function. This new mathematical approach can be useful in viscoelasticity and diffusion processes in order to consider time-dependent coefficients. We are able to find the exact analytic solution of the creep experiment based on our new approach and we can compare it with the results obtained by Zhou et al.