<p>Traditional integer-order models often fall short in capturing the complex, memory-dependent behaviours of viscoelastic materials. As a result, fractional calculus has become an essential tool for modelling viscoelastic materials, which exhibit both solid and fluid-like properties. This work presents a concise review of fractional viscoelastic models, tracing their evolution through distinct generations, with a particular emphasis on the most recent generations. After a thorough analysis of the proposed models, the manuscript offers valuable insights into promising directions for future research while critically evaluating past developments. These insights are intended to deepen and broaden the understanding of the full spectrum of complex viscoelastic behaviours while fostering critical thinking about the use of generalized derivative and integral operators of any kind.</p>

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Fractional Derivatives: the ultimate operator for modelling complex viscoelastic materials?

  • Luís L. Ferrás

摘要

Traditional integer-order models often fall short in capturing the complex, memory-dependent behaviours of viscoelastic materials. As a result, fractional calculus has become an essential tool for modelling viscoelastic materials, which exhibit both solid and fluid-like properties. This work presents a concise review of fractional viscoelastic models, tracing their evolution through distinct generations, with a particular emphasis on the most recent generations. After a thorough analysis of the proposed models, the manuscript offers valuable insights into promising directions for future research while critically evaluating past developments. These insights are intended to deepen and broaden the understanding of the full spectrum of complex viscoelastic behaviours while fostering critical thinking about the use of generalized derivative and integral operators of any kind.