Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 46, Issue 1, Pages 368-387Publisher
WILEY
DOI: 10.1002/mma.8516
Keywords
distributed order fractional derivatives; fractional calculus; Laplace transform; Maxwell model; viscoelasticity
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In this work, a generalised viscoelastic model using distributed-order derivatives is presented, allowing for a more accurate description of complex fluids. By choosing a proper weighting function of the order of the derivatives, this model generalises the fractional viscoelastic model and establishes connections between classical, fractional and distributed-order viscoelastic models.
In this work, we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented by Schiessel and Blumen and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. We discuss the connection between classical, fractional and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. We also derive the relaxation modulus, the storage and loss modulus and the creep compliance for specific weighting functions.
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