Nutting,
P. G.
, 1921, “
A New General Law of Deformation,” J. Frank. Inst.,
191(5), pp. 679–685.

[CrossRef]
Di Paola,
M.
,
Pirrotta,
A.
, and
Valenza,
A.
, 2011, “
Visco-Elastic Behavior Through Fractional Calculus: An Easier Method for Best Fitting Experimental Results,” Mech. Mater.,
43(12), pp. 799–806.

[CrossRef]
Di Paola,
M.
,
Fiore,
V.
,
Pinnola,
F. P.
, and
Valenza,
A.
, 2014, “
On the Influence of the Initial Ramp for a Correct Definition of the Parameters of Fractional Viscoelastic Materials,” Mech. Mater.,
69(1), pp. 63–70.

[CrossRef]
Gemant,
A.
, 1936, “
A Method of Analyzing Experimental Results Obtained From Elasto-Viscous Bodies,” J. Phys.,
7(8), pp. 311–317.

Scott Blair,
G. W.
, and
Caffyn,
J. E.
, 1949, “
An Application of the Theory of Quasi-Properties to the Treatment of Anomalous Strain-Stress Relations,” Philos. Mag.,
40(300), pp. 80–94.

[CrossRef]
Caputo,
M.
, 1967, “
Linear Models of Dissipation Whose Q Is Almost Frequency Independent-II,” Geophys. J. R. Astron. Soc.,
13(5), pp. 529–539.

[CrossRef]
Caputo,
M.
, 1969, Elasticità e Dissipazione,
Zanichelli,
Bologna, Italy.

Bagley,
R. L.
, and
Torvik,
P. J.
, 1986, “
On the Fractional Calculus Model of Viscoelastic Behavior,” J. Rheol.,
30(1), pp. 133–155.

[CrossRef]
Schiessel,
H.
, and
Blumen,
A.
, 1993, “
Hierarchical Analogues to Fractional Relaxation Equations,” J. Phys. A Math. Gen.,
26(19), pp. 5057–5069.

[CrossRef]
Heymans,
N.
, and
Bauwens,
J. C.
, 1994, “
Fractal Rheological Models and Fractional Differential Equations for Viscoelastic Behavior,” Rheol. Acta,
33(3), pp. 210–219.

[CrossRef]
Soczkiewicz,
K.
, 2002, “
Application of Fractional Calculus in the Theory of Viscoelasticity,” Mol. Quantum Acoust.,
23, pp. 397–404.

Mainardi,
F.
, 2010, Fractional Calculus and Waves in Linear Viscoelasticity An Introduction to Mathematical Models,
Imperial College Press,
London.

Alotta,
G.
,
Di Paola,
M.
, and
Pirrotta,
A.
, 2014, “
Fractional Tajimi-Kanai Model for Simulating Earthquake Ground Motion,” Bull. Earthquake Eng.,
12(6), pp. 2495–2506.

[CrossRef]
Alotta,
G.
,
Failla,
G.
, and
Zingales,
M.
, 2015, “
Finite-Element Formulation of a Nonlocal Hereditary Fractional-Order Timoshenko Beam,” ASCE J. Eng. Mech.,
143(5), epub.

Alotta,
G.
,
Barrera,
O.
,
Cocks,
A. C. F.
, and
Di Paola,
M.
, 2016, “
On the Behavior of a Three-Dimensional Fractional Viscoelastic Constitutive Model,” Meccanica, epub.

Di Paola,
M.
,
Pinnola,
F. P.
, and
Zingales,
M.
, 2013, “
A Discrete Mechanical Model of Fractional Hereditary Materials,” J. Mecc.,
48(7), pp. 1573–1586.

[CrossRef]
Di Paola,
M.
,
Pinnola,
F. P.
, and
Zingales,
M.
, 2013, “
Fractional Differential Equations and Related Exact Mechanical Models,” Comput. Math. Appl.,
66(5), pp. 608–620.

[CrossRef]
Di Mino,
G.
,
Airey,
G.
,
Di Paola,
M.
,
Pinnola,
F. P.
,
D'Angelo,
G.
, and
Lo Presti,
D.
, 2016, “
Linear and Nonlinear Fractional Hereditary Constitutive Laws of Asphalt Mixtures,” J. Civil Eng. Manage.,
22(7), pp. 882–889.

[CrossRef]
Colinas-Armijo,
N.
,
Cottone,
G.
, and
Di Paola,
M.
, 2016, “
Viscoelastic Modeling by Katugampola Fractional Derivative,” Tenth International Conference on the Mechanics of Time Dependent Materials, Paris, France, May 17–20.

Di Lorenzo,
S.
,
Di Paola,
M.
,
Pinnola,
F. P.
, and
Pirrotta,
A.
, 2013, “
Stochastic Response of Fractionally Damped Beams,” Probab. Eng. Mech.,
35, pp. 37–43.

[CrossRef]
Pirrotta,
A.
,
Cutrona,
S.
, and
Di Lorenzo,
S.
, 2015, “
Fractional Visco-Elastic Timoshenko Beam From Elastic Euler-Bernoulli Beam,” Acta Mech.,
226(1), pp. 179–189.

[CrossRef]
Spanos,
P. D.
, and
Evangelatos,
G. I.
, 2010, “
Response of a Non-Linear System With Restoring Forces Governed by Fractional Derivatives-Time Domain Simulation and Statistical Linearization Solution,” Soil Dyn. Earthquake Eng.,
30(9), pp. 811–821.

[CrossRef]
Di Paola,
M.
,
Failla,
G.
, and
Pirrotta,
A.
, 2012, “
Stationary and Non-Stationary Stochastic Response of Linear Fractional Viscoelastic Systems,” Probab. Eng. Mech.,
28, pp. 85–90.

[CrossRef]
Colinas-Armijo,
N.
,
Di Paola,
M.
, and
Pinnola,
F. P.
, 2016, “
Fractional Characteristic Times and Dissipated Energy in Fractional Linear Viscoelasticity,” Commun. Nonlinear Sci. Numer. Simul.,
37, pp. 14–30.

[CrossRef]
Williams,
M. L.
,
Landel,
R. F.
, and
Ferry,
J. D.
, 1955, “
The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids,” J. Am. Chem. Soc.,
77(14), pp. 3701–3707.

[CrossRef]
Gross,
B.
, 1968, Mathematical Structure of the Theories of Viscoelasticity,
Hermann et Cie,
Paris, France.

Ferry,
J. D.
, 1980, Viscoelastic Properties of Polymers,
Wiley, New York.

Dealy,
J.
, and
Plazek,
D.
, 2009, “
Time-Temperature Superposition—A Users Guide,” J. Rheol. Bull.,
78(2), pp. 16–31.

Bueche,
F.
, 1954, “
The Viscoelastic Properties of Plastics,” J. Chem. Phys.,
22(4), pp. 603–609.

[CrossRef]
Podlubny,
I.
, 2000, “
Matrix Approach to Discrete Fractional Calculus,” Fract. Calculus Appl. Anal.,
3(4), pp. 359–386.

Christensen,
R. M.
, 1982, Theory of Viscoelasticity,
Academic Press,
New York.

Podlubny,
I.
, 1999, Fractional Differential Equations,
Academic Press,
San Diego, CA.

Schiessel,
H.
,
Metzler,
R.
,
Blumen,
A.
, and
Nonnenmacher,
T. F.
, 1995, “
Generalized Viscoelastic Models: Their Fractional Equations With Solutions,” J. Phys. A: Math. Gen.,
28(23), pp. 6567–6584.

[CrossRef]
Badagliacco,
D.
,
Colinas-Armijo,
N.
,
Di Paola,
M.
, and
Valenza,
A.
, 2016, “
Evaluation of the Temperature Effect on the Fractional Linear Viscoelastic Model for an Epoxy Resin,” AIP Conf. Proc.,
1736(1), p. 020089.

Badagliacco,
D.
,
Colinas-Armijo,
N.
,
Di Paola,
M.
, and
Valenza,
A.
, 2017, “
Time-Temperature Superposition Principle Through Fractional Characteristic Times - Experimental Evidence on Epoxy Resin,” J. Mech. Phys. Solids, (submitted).

Horn,
R. A.
, and
Johnson,
C. R.
, 1991, Topics in Matrix Analysis,
Cambridge University Press,
Cambridge, UK.