On variable-order fractional linear viscoelasticity
Andrea Giusti, Ivano Colombaro, Roberto Garra, Roberto Garrappa, Andrea Mentrelli
Abstract
Abstract A generalization of fractional linear viscoelasticity based on Scarpi’s approach to variable-order fractional calculus is presented. After reviewing the general mathematical framework, a variable-order fractional Maxwell model is analysed as a prototypical example for the theory. Some physical considerations are then provided concerning the fractionalisation procedure and the choice of the transition functions. Lastly, the material functions for the considered model are derived and numerically evaluated for exponential-type and Mittag-Leffler-type order functions.
Topics & Concepts
ViscoelasticityOrder (exchange)Variable (mathematics)MathematicsApplied mathematicsMathematical analysisPhysicsThermodynamicsEconomicsFinanceFractional Differential Equations SolutionsRheology and Fluid Dynamics StudiesNanofluid Flow and Heat Transfer