Dedicated to Professor Stanislav Meshkov on the occasion of his 75th birthday

Interest in fractional calculus has quickened profoundly in the past few decades, resulting in a large body of articles devoted to this challenge, and sometimes researchers, especially young ones, who have tried to or will attempt the fractional calculus in problems of mechanics, may be hard pressed to orient themselves in such information explosion. Thus, as a result, certain findings are rediscovered, references are cited improperly or even incorrectly, priorities are placed erroneously, and some results remain concealed. In this connection, a story about two papers dealing with fractional calculus application in mechanics is rather instructive.

The first paper to be under consideration is “A New Dissipation Model Based on Memory Mechanism” by the Italian researchers Caputo and Mainardi (1), which was submitted in March 5, 1971...

1.
Caputo
,
M.
, and
Mainardi
,
F.
, 1971, “
A New Dissipation Model Based on Memory Mechanism
,”
Pure Appl. Geophys.
0033-4553,
91
(
1
), pp.
134
147
(DOI 10.1007/BF00879562, published online 29 Dec. 2004).
2.
Meshkov
,
S. I.
,
Pachevskaya
,
G. N.
,
Postnikov
,
V. S.
, and
Rossikhin
,
Y. A.
, 1971, “
Integral Representation of ∍γ-Functions and Their Application to Problems in Linear Viscoelasticity
,”
Int. J. Eng. Sci.
0020-7225,
9
, pp.
387
398
(DOI 10.1016/0020-7225(71)90059-0, published online 27 Feb. 2003 in ScienceDirect) .
3.
Mainardi
,
F.
, 1997, private communication.
4.
Mainardi
,
F.
, 2007, private communication.
5.
Rossikhin
,
Y. A.
, 2007, private communication.
6.
Caputo
,
M.
, and
Mainardi
,
F.
, 2007, “Reprinted Paper From the Journal Pure and Applied Geophysics (PAGEOPH), 1971, 91(1), pp. 134–147,”
Fractional Calculus Appl. Anal.
1311-0454,
10
(
3
), pp.
309
324
.
7.
Kiryakova
,
V.
, 2007, “Editorial Note,”
Fractional Calculus Appl. Anal.
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10
(
3
), p.
309
.
8.
Caputo
,
M.
, 2008, “Reprinted Paper From the Journal Geophys. J. R. Astr. Soc., 13(5), pp. 529–539,”
Fractional Calculus Appl. Anal.
1311-0454,
11
(
1
), pp.
4
14
.
9.
Caputo
,
M.
, 1967, “
Linear Models of Dissipation Whose Q is Almost Frequency Independent—II
,”
Geophys. J. R. Astron. Soc.
0016-8009,
13
(
5
), pp.
529
539
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10.
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,
V.
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Fractional Calculus Appl. Anal.
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), p.
3
.
11.
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,
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,”
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.
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,
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,”
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,
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,”
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21
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.
14.
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,
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,
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,
B. C.
, and
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,
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,”
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,
D. R.
, 1960,
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, Vol.
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,
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,
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Rabotnov
,
Y. N.
, 1969, “
Creep Problems in Structural Members
,”
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, Vol.
7
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,
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.
17.
Dzherbashian
,
M. M.
, and
Nersesian
,
A. B.
, 1968, “
Fractional Derivatives and the Cauchy Problem for Differential Equations of Fractional Order
,”
Izvestija Academii Nauk Armjanskoi SSR, Matematika
,
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, pp.
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29
.
18.
Caputo
,
M.
, 1974, “
Vibrations of an Infinite Viscoelastic Layer With a Dissipative Memory
,”
J. Acoust. Soc. Am.
0001-4966,
56
(
3
), pp.
897
904
(DOI 10.1121/1.1903344).
19.
Caputo
,
M.
, 1976, “
Vibrations of an Infinite Plate With a Frequency Independent Q
,”
J. Acoust. Soc. Am.
0001-4966,
60
(
3
), pp.
634
639
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20.
Butzer
,
P. L.
, and
Westphal
,
U.
, 2000, “
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,”
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,
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, ed.,
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,
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, pp.
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85
.
21.
Freed
,
A. D.
, and
Diethelm
,
K.
, 2007, “
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,”
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1311-0454,
10
(
3
), pp.
219
248
.
22.
Meshkov
,
S. I.
,
Pachevskaya
,
G. N.
, and
Shermergor
,
T. D.
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,”
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), pp.
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65
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23.
Meshkov
,
S. I.
, and
Pachevskaya
,
G. N.
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,”
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), pp.
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48
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Meshkov
,
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,”
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), pp.
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Meshkov
,
S. I.
, and
Rossikhin
,
Y. A.
, 1968, “
Propagation of Acoustic Waves in a Hereditarily Elastic Medium
,”
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9
(
5
), pp.
589
592
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26.
Meshkov
,
S. I.
, 1969, “
On the Steady Regime of an Hereditarily Elastic Oscillator
,”
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10
(
5
), pp.
780
785
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27.
Meshkov
,
S. I.
, 1970, “
The Integral Representation of Fractionally Exponential Functions and Their Application to Dynamic Problems of Linear Visco-Elasticity
,”
J. Appl. Mech. Tech. Phys.
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11
(
1
), pp.
100
107
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28.
Zelenev
,
V. M.
,
Meshkov
,
S. I.
, and
Rossikhin
,
Y. A.
, 1970, “
Damped Vibrations of Hereditary-Elastic Systems With Weakly Singular Kernels
,”
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11
(
2
), pp.
290
293
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29.
Meshkov
,
S. I.
, 1970, “
Stationary Mode of a Nonlinear Elastically Hereditary Oscillator
,”
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11
(
3
), pp.
458
462
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30.
Zelenev
,
V. M.
,
Meshkov
,
S. I.
, and
Rossikhin
,
Y. A.
, 1970, “
Effect of the ∍-function Singularity Parameters on the Damped Vibrations of Elastic Systems With Aftereffect
,”
Mech. Solids
0025-6544,
5
(
3
), pp.
92
94
.
31.
Astaf’ev
,
V. I.
, and
Meshkov
,
S. I.
, 1970, “
Forced Oscillations of a Semi-Infinite Bar Made From a Nonlinear Hereditarily Elastic Material
,”
Mech. Solids
0025-6544,
5
(
4
), pp.
82
86
.
32.
Meshkov
,
S. I.
, and
Rossikhin
,
Y. A.
, 1971, “
Temperature Dependence of the Damping Coefficients for a Dynamical System With a Singular Kernel
,”
J. Eng. Phys. Thermophys.
1062-0125,
21
(
2
), p.
1090
(DOI 10.1007/BF00825526, published online 13 Dec. 2004 in SpringerLink) .
33.
Gonsovskii
,
V. L.
,
Meshkov
,
S. I.
, and
Rossikhin
,
Y. A.
, 1972, “
Impact of a Viscoelastic Rod Onto a Rigid Target
,”
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), pp.
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1113
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34.
Rossikhin
,
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, 1970, “
Dynamic Problems of Linear Viscoelasticity Connected With the Investigation of Retardation and Relaxation Spectra (in Russian)
,” Ph.D. thesis, Voronezh Polytechnic Institute, Voronezh, Russia.
35.
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,
M.
, and
Mainardi
,
F.
, 1971, “
Linear Models of Dissipation in Anelastic Solids
,”
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1
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),
161
198
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36.
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,
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, and
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,”
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37.
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,
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,
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,
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Thermal Stresses in Concrete Solid Masses With Due Account for Creep in Concrete
,
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,”
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