An original perspective on variable-order fractional operators for viscoelastic materials

[1]  Vincenzo Fiore,et al.  On the influence of the initial ramp for a correct definition of the parameters of fractional viscoelastic materials , 2014 .

[2]  I. Podlubny Fractional differential equations , 1998 .

[3]  Carlos F.M. Coimbra,et al.  The variable viscoelasticity oscillator , 2005 .

[4]  Nagehan Demirci,et al.  Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation. , 2014, Acta of bioengineering and biomechanics.

[5]  G. Alotta,et al.  A novel approach to nonlinear variable-order fractional viscoelasticity , 2020, Philosophical Transactions of the Royal Society A.

[6]  H. Pu,et al.  Variable-order fractional creep model of mudstone under high-temperature , 2017 .

[7]  A high-speed algorithm for computation of fractional differentiation and fractional integration , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  A. Pirrotta,et al.  Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results , 2011 .

[9]  R. Metzler,et al.  Generalized viscoelastic models: their fractional equations with solutions , 1995 .

[10]  G. Alotta,et al.  Analysis of Fractional Viscoelastic Material With Mechanical Parameters Dependent on Random Temperature , 2017 .

[11]  Mario Di Paola,et al.  On the dynamics of non-local fractional viscoelastic beams under stochastic agencies , 2018 .

[12]  Hongguang Sun,et al.  A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications , 2019, Fractional Calculus and Applied Analysis.

[13]  G. Alotta,et al.  Finite-Element Formulation of a Nonlocal Hereditary Fractional-Order Timoshenko Beam , 2017 .

[14]  Huiyu Sun,et al.  Application of fractional calculus methods to viscoelastic behaviours of solid propellants , 2020, Philosophical Transactions of the Royal Society A.

[15]  R. Caponetto,et al.  Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids , 2020, Philosophical Transactions of the Royal Society A.

[16]  B. Ross,et al.  Integration and differentiation to a variable fractional order , 1993 .

[17]  W. Chen,et al.  A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems , 2011 .

[18]  D. Zorica,et al.  A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete , 2018 .

[19]  Deshun Yin,et al.  Fractional description of time-dependent mechanical property evolution in materials with strain softening behavior , 2016 .

[20]  A. Pirrotta,et al.  Fractional Tajimi–Kanai model for simulating earthquake ground motion , 2014, Bulletin of Earthquake Engineering.

[21]  P. G. Nutting,et al.  A new general law of deformation , 1921 .

[22]  Ruifan Meng,et al.  A variable order fractional constitutive model of the viscoelastic behavior of polymers , 2019, International Journal of Non-Linear Mechanics.

[23]  R. Bagley,et al.  On the Appearance of the Fractional Derivative in the Behavior of Real Materials , 1984 .

[24]  M. Granata,et al.  Fractional model of concrete hereditary viscoelastic behaviour , 2017 .

[25]  R. Bagley,et al.  On the Fractional Calculus Model of Viscoelastic Behavior , 1986 .

[26]  R. Guedes A viscoelastic model for a biomedical ultra-high molecular weight polyethylene using the time–temperature superposition principle , 2011 .

[27]  Carlos F.M. Coimbra,et al.  A variable order constitutive relation for viscoelasticity , 2007 .

[28]  G. Alotta,et al.  On the behavior of a three-dimensional fractional viscoelastic constitutive model , 2017 .

[29]  Alberto Di Matteo,et al.  Fractional viscoelastic behaviour under stochastic temperature process , 2017, Probabilistic Engineering Mechanics.

[30]  M. Enelund,et al.  Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws , 1999 .

[31]  Fabio Semperlotti,et al.  Applications of variable-order fractional operators: a review , 2020, Proceedings of the Royal Society A.

[32]  Tom Scarpas,et al.  Studies on creep and recovery of rheological bodies based upon conventional and fractional formulations and their application on asphalt mixture , 2008 .

[33]  Carlos F.M. Coimbra,et al.  Mechanics with variable‐order differential operators , 2003 .