Based on the differential conformal transformation in the fractional order, we defined the fractional memristor in contrast to the traditional (integer-order) memristor. As an example, a typical spin-transfer torque (STT) memristor (with the asymmetric resistance hysteresis) was proved to be a 0.8 fractional memristor. In conclusion, many memristors should not be treated as ideal ones due to the fractional interaction between flux and charge. Indeed, unless a non-ideal memristor is properly modelled as a fractional memristor, no deep physical understanding would be possible to develop a reliable commercial product.

1.
L.
Chua
, “
Memristor—the missing circuit element
,”
IEEE Trans. Circuit Theory
18
(
5
),
507
519
(
1971
).
2.
K. B.
Oldham
and
J.
Spanier
,
The Fractional Calculus
(
Academic Press
,
New York
,
1974
).
3.
I.
Podlubny
,
Fractional Differential Equations
(
Academic Press
,
San Diego
,
1999
).
4.
I.
Petras
,
I.
Podlubny
,
P.
O'Leary
,
L.
Dorcak
, and
B.
Vinagre
,
Analogue Realization of Fractional Order Controllers
(
FBERG Technical University of Kosice
,
2002
).
5.
M.
Abdelouahab
,
R.
Lozi
, and
L.
Chua
, “
Memfractance: A mathematical paradigm for circuit elements with memory
,”
Int. J. Bifurcation Chaos
24
,
1430023
(
2014
).
6.
J. C.
Slonczewski
, “
Current-driven excitation of magnetic multilayers
,”
J. Magnetism Magnetic Mater.
159
(
1–2
),
L1
(
1996
).
7.
L.
Berger
, “
Emission of spin waves by a magnetic multilayer traversed by a current
,”
Phys. Rev. B
54
,
9353
(
1996
).
8.
G. D.
Fuchs
,
N. C.
Emley
,
I. N.
Krivorotov
,
P. M.
Braganca
,
E. M.
Ryan
,
S. I.
Kiselev
,
J. C.
Sankey
,
D. C.
Ralph
,
R. A.
Buhrman
, and
J. A.
Katine
, “
Spin-Transfer Effects in Nanoscale Magnetic Tunnel Junctions
,”
Appl. Phys. Lett.
85
,
1205
1207
(
2004
).
9.
Y.
Huai
,
D.
Apalkov
,
Z.
Diao
,
Y.
Ding
, and
A.
Panchula
, “
Structure, materials and shape optimization of magnetic tunnel junction devices: Spin-transfer switching current reduction for future magnetoresistive random access memory
,”
Jpn. J. Appl. Phys.
45
(
5A
),
3835
3841
(
2006
).
10.
X.
Li
,
Z.
Zhang1
,
Q. Y.
Jin
, and
Y.
Liu
, “
Spin-torque-induced switching in a perpendicular GMR nanopillar with a soft core inside the free layer
,”
New J. Phys.
11
,
023027
(
2009
).
11.
H.
Meng
and
J.
Wang
, “
Asymmetric spin torque transfer in nano GMR Device with perpendicular anisotropy
,”
IEEE Trans. Magn.
43
(
6
),
2833
(
2007
).
12.
F. Z.
Wang
, “
A triangular periodic table of elementary circuit elements
,”
IEEE Trans. Circuits Syst.
60
(
3
),
616
623
(
2013
).
13.
L.
Chua
, “
Resistance switching memories are memristors
,”
Appl. Phys. A
102
(
4
),
765
783
(
2011
).
14.
L.
Chua
, “
If it's pinched it's a memristor
,”
Semicond. Sci. Technol.
29
(
10
),
104001
(
2014
).
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