-
3
-
-
0002128448
-
Fractional calculus
-
Ross B. Fractional calculus. Math Mag 1977, 50(3):115-122.
-
(1977)
Math Mag
, vol.50
, Issue.3
, pp. 115-122
-
-
Ross, B.1
-
4
-
-
33749508781
-
Les différentielles métaphysiques (histoire et philosophie de la généralisation de l'ordre de dérivation) Thèse
-
Université Paris Nord, Paris
-
Dugowson S. Les différentielles métaphysiques (histoire et philosophie de la généralisation de l'ordre de dérivation) Thèse, Université Paris Nord, Paris 1994.
-
(1994)
-
-
Dugowson, S.1
-
6
-
-
0004164347
-
-
The Johns Hopkins University Press, Baltimore, London
-
Nahin P.J. Oliver heaviside: the life, work, and times of an electrical genius of the victorian age 2002, The Johns Hopkins University Press, Baltimore, London.
-
(2002)
Oliver heaviside: the life, work, and times of an electrical genius of the victorian age
-
-
Nahin, P.J.1
-
8
-
-
0000595654
-
-
Segré E., editor. Published later in Collected Papers of Enrico Fermi, University of Chicago Press, Los Alamos report LA-1940
-
Fermi SUE, Pasta J. Studies of nonlinear problems. In: Segré E., editor. Published later in Collected Papers of Enrico Fermi, University of Chicago Press, Los Alamos report LA-1940, 1965.
-
(1965)
Studies of nonlinear problems
-
-
Fermi, S.U.E.1
Pasta, J.2
-
9
-
-
0347371015
-
The fermi-pasta-ulam problem: paradox turns discovery
-
Ford J. The fermi-pasta-ulam problem: paradox turns discovery. Phys. Rep. 1992, 213(5):271-310.
-
(1992)
Phys. Rep.
, vol.213
, Issue.5
, pp. 271-310
-
-
Ford, J.1
-
11
-
-
67649515529
-
Fermi, pasta, ulam and the birth of experimental mathematics
-
Hu B., Campbell D.K., Porter M.A., Zabusky N.J. Fermi, pasta, ulam and the birth of experimental mathematics. Amer Sci 2009, 97(6):214-221.
-
(2009)
Amer Sci
, vol.97
, Issue.6
, pp. 214-221
-
-
Hu, B.1
Campbell, D.K.2
Porter, M.A.3
Zabusky, N.J.4
-
12
-
-
0015127532
-
Memristor - the missing circuit element
-
Chua L.O. Memristor - the missing circuit element. IEEE Trans Circ Theory 1971, 18(2):507-519.
-
(1971)
IEEE Trans Circ Theory
, vol.18
, Issue.2
, pp. 507-519
-
-
Chua, L.O.1
-
13
-
-
43049126833
-
The missing memristor found
-
Stewart Duncan R., Stanley Williams R., Strukov Dmitri B., Snider Gregory S. The missing memristor found. Nature 2008, 97:80-83.
-
(2008)
Nature
, vol.97
, pp. 80-83
-
-
Stewart, D.R.1
Stanley Williams, R.2
Strukov, D.B.3
Snider, G.S.4
-
14
-
-
0003797958
-
Fractional differential equations
-
Academic Press, San Diego, An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution
-
Podlubny I. Fractional differential equations. Mathematics in Science and Engineering 1998, vol. 198. Academic Press, San Diego.
-
(1998)
Mathematics in Science and Engineering
, vol.198
-
-
Podlubny, I.1
-
19
-
-
0011918058
-
On operators in physical mathematics
-
Heaviside O. On operators in physical mathematics. Proc Roy Soc 1893, 52:504-529.
-
(1893)
Proc Roy Soc
, vol.52
, pp. 504-529
-
-
Heaviside, O.1
-
20
-
-
0345218900
-
A method of analyzing experimental results obtained from elasto-viscous bodies
-
Gemant A. A method of analyzing experimental results obtained from elasto-viscous bodies. Physics 1936, 7:311-317.
-
(1936)
Physics
, vol.7
, pp. 311-317
-
-
Gemant, A.1
-
21
-
-
0001552054
-
On fractional differentials
-
Gemant A. On fractional differentials. Philos Mag 1938, 25:540-549.
-
(1938)
Philos Mag
, vol.25
, pp. 540-549
-
-
Gemant, A.1
-
22
-
-
33750042937
-
Analithical and integrative aspects of the stress-strain-time problem
-
Blair G.W.S. Analithical and integrative aspects of the stress-strain-time problem. J Sci Instrum 1944, 21(5):80-84.
-
(1944)
J Sci Instrum
, vol.21
, Issue.5
, pp. 80-84
-
-
Blair, G.W.S.1
-
23
-
-
50349117552
-
The role of psychophysics in rheology
-
Blair G.W.S. The role of psychophysics in rheology. J Colloid Sci 1947, 2(1):21-32.
-
(1947)
J Colloid Sci
, vol.2
, Issue.1
, pp. 21-32
-
-
Blair, G.W.S.1
-
24
-
-
0010173982
-
Fractional Calculus and Its Applications
-
New Haven, Springer-Verlag, New York
-
Ross B. editor. Fractional Calculus and Its Applications. Proceedings of the International Conference, New Haven, Springer-Verlag, New York, 1974.
-
(1974)
Proceedings of the International Conference
-
-
Ross, B.1
-
27
-
-
85153917485
-
-
World Scientific, Singapore
-
Fortuna L., Petras I., Caponetto Riccardo, Dongola Giovanni Fractional order systems: modeling and control applications 2010, World Scientific, Singapore.
-
(2010)
Fractional order systems: modeling and control applications
-
-
Fortuna, L.1
Petras, I.2
Caponetto, R.3
Dongola, G.4
-
28
-
-
79952143317
-
-
Springer, London
-
Vinagre Blas M., Xue Dinguü, Feliu Vicente, Monje Concepción Alicia, Chen YangQuan Fractional-order systems and controls 2010, Springer, London.
-
(2010)
Fractional-order systems and controls
-
-
Vinagre, B.M.1
Xue Dinguü2
Feliu, V.3
Monje, C.A.4
Chen, Y.5
-
31
-
-
0030651602
-
Analysis and design of fractional-order digital control systems
-
Machado J.A.T. Analysis and design of fractional-order digital control systems. Syst Anal Model Simul 1997, 27(2-3):107-122.
-
(1997)
Syst Anal Model Simul
, vol.27
, Issue.2-3
, pp. 107-122
-
-
Machado, J.A.T.1
-
34
-
-
84885710343
-
-
Springer, Dordrecht, The Netherlands
-
Tenreiro Machado J.A., Sabatier Jocelyn, Agrawal Om Prakash Advances in fractional calculus: theoretical developments and applications in physics and engineering 2007, Springer, Dordrecht, The Netherlands.
-
(2007)
Advances in fractional calculus: theoretical developments and applications in physics and engineering
-
-
Tenreiro Machado, J.A.1
Sabatier, J.2
Agrawal, O.P.3
-
37
-
-
0000162804
-
The relationship between fractional calculus and fractals
-
Tatom F.B. The relationship between fractional calculus and fractals. Fractals 1995, 3(1):217-229.
-
(1995)
Fractals
, vol.3
, Issue.1
, pp. 217-229
-
-
Tatom, F.B.1
-
38
-
-
0242354999
-
Geometric and physical interpretation of fractional integration and fractional differentiation
-
Podlubny I. Geometric and physical interpretation of fractional integration and fractional differentiation. J Fract Calc Appl Anal 2002, 5(4):367-386.
-
(2002)
J Fract Calc Appl Anal
, vol.5
, Issue.4
, pp. 367-386
-
-
Podlubny, I.1
-
39
-
-
14844296496
-
A probabilistic interpretation of the fractional-order differentiation
-
Machado J.A.T. A probabilistic interpretation of the fractional-order differentiation. J Fract Calc Appl Anal 2003, 6(1):73-80.
-
(2003)
J Fract Calc Appl Anal
, vol.6
, Issue.1
, pp. 73-80
-
-
Machado, J.A.T.1
-
40
-
-
63449116783
-
Fractional derivatives: probability interpretation and frequency response of rational approximations
-
Machado J.A.T. Fractional derivatives: probability interpretation and frequency response of rational approximations. Commun Nonlinear Sci Numer Simul 2009, 14(9-10):3492-3497.
-
(2009)
Commun Nonlinear Sci Numer Simul
, vol.14
, Issue.9-10
, pp. 3492-3497
-
-
Machado, J.A.T.1
-
41
-
-
80052654574
-
Mittag-leffler functions and their applications
-
Saxena R.K., Haubold H.J., Mathai A.M. Mittag-leffler functions and their applications. J Appl Math 2011, 2011:51. 10.1155/2011/298628.
-
(2011)
J Appl Math
, vol.2011
, pp. 51
-
-
Saxena, R.K.1
Haubold, H.J.2
Mathai, A.M.3
-
42
-
-
0032665414
-
Fractional-order derivative approximations in discrete-time control systems
-
Machado J.A.T. Fractional-order derivative approximations in discrete-time control systems. Syst Anal Model Simul 1999, 34:419-434.
-
(1999)
Syst Anal Model Simul
, vol.34
, pp. 419-434
-
-
Machado, J.A.T.1
-
45
-
-
0010174001
-
On the realization of a constant-argument immitance of fractional operator
-
Roy S.C.D. On the realization of a constant-argument immitance of fractional operator. IEEE Trans Circ Theory 1967, 14(3):264-374.
-
(1967)
IEEE Trans Circ Theory
, vol.14
, Issue.3
, pp. 264-374
-
-
Roy, S.C.D.1
-
47
-
-
85196167528
-
-
Dead matter has memory. Causal consulting, Kalmar, Sweden, 2002.
-
Westerlund S. Dead matter has memory. Causal consulting, Kalmar, Sweden, 2002.
-
-
-
Westerlund, S.1
-
48
-
-
13644250291
-
Analog realization of a fractional control element - revisited
-
on Decision and Control, Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics, Las Vegas, USA
-
Bohannan GW. Analog realization of a fractional control element - revisited. In: Proc. of the 41st IEEE Int. Conf. on Decision and Control, Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics, Las Vegas, USA, 2002.
-
(2002)
Proc. of the 41st IEEE Int. Conf.
-
-
Bohannan, G.W.1
-
49
-
-
34047142616
-
Realization of a constant phase element and its performance study in a differentiator circuit
-
Dutta P.K., Biswas K., Sen S. Realization of a constant phase element and its performance study in a differentiator circuit. IEEE Trans Circ Syst II: Express Briefs 2006, 53(9):802-806.
-
(2006)
IEEE Trans Circ Syst II: Express Briefs
, vol.53
, Issue.9
, pp. 802-806
-
-
Dutta, P.K.1
Biswas, K.2
Sen, S.3
-
50
-
-
85196153565
-
Fractional calculus analysis of the electrical skin phenomena
-
Springer, Dordrecht, The Netherlands, O.P. Agrawal, J. Sabatier, J. Tenreiro Machado (Eds.)
-
Galhano Alexandra M., Boaventura Cunha J., Tenreiro Machado J.A., Jesus Isabel S. Fractional calculus analysis of the electrical skin phenomena. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering 2007, 323-332. Springer, Dordrecht, The Netherlands. O.P. Agrawal, J. Sabatier, J. Tenreiro Machado (Eds.).
-
(2007)
Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering
, pp. 323-332
-
-
Galhano, A.M.1
Boaventura Cunha, J.2
Tenreiro Machado, J.A.3
Jesus, I.S.4
-
51
-
-
38949212151
-
Modelling of lossy coils using fractional derivatives
-
045001
-
Krüger Klaus, Schafer I. Modelling of lossy coils using fractional derivatives. J Phys D: Appl Phys 2008, 41(045001):1-8.
-
(2008)
J Phys D: Appl Phys
, vol.41
, pp. 1-8
-
-
Krüger, K.1
Schafer, I.2
-
52
-
-
61449144602
-
Development of fractional order capacitors based on electrolyte processes
-
Jesus I.S., Machado J.A.T. Development of fractional order capacitors based on electrolyte processes. Nonlinear Dynam 2009, 56(1-2):45-55.
-
(2009)
Nonlinear Dynam
, vol.56
, Issue.1-2
, pp. 45-55
-
-
Jesus, I.S.1
Machado, J.A.T.2
-
53
-
-
84858707796
-
Fractional order inductive phenomena based on the skin effect
-
Galhano Alexandra M., Tenreiro Machado J.A. Fractional order inductive phenomena based on the skin effect. Nonlinear Dynam. 2012, 68(1-2):107-115.
-
(2012)
Nonlinear Dynam.
, vol.68
, Issue.1-2
, pp. 107-115
-
-
Galhano, A.M.1
Tenreiro Machado, J.A.2
-
55
-
-
76449092011
-
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized mittag-leffler stability
-
Podlubny Igor, Li Yan, Chen YangQuan Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized mittag-leffler stability. Comput Math Appl 2010, 59(5):1810-1821.
-
(2010)
Comput Math Appl
, vol.59
, Issue.5
, pp. 1810-1821
-
-
Podlubny, I.1
Li, Y.2
Chen, Y.3
-
57
-
-
79960253662
-
Fractional dynamics of a system with particles subjected to impacts
-
Machado J.A.T. Fractional dynamics of a system with particles subjected to impacts. Commun Nonlinear Sci Numer Simul 2011, 16(12):4596-4601.
-
(2011)
Commun Nonlinear Sci Numer Simul
, vol.16
, Issue.12
, pp. 4596-4601
-
-
Machado, J.A.T.1
-
59
-
-
0019079281
-
Device modeling via basic nonlinear circuits elements
-
Kang Sung-Mo, Chua Leon O. Device modeling via basic nonlinear circuits elements. IEEE Trans Circ Syst 1980, 27(11):1014-1044.
-
(1980)
IEEE Trans Circ Syst
, vol.27
, Issue.11
, pp. 1014-1044
-
-
Kang, S.-M.1
Chua, L.O.2
-
61
-
-
0016918810
-
Memristive devices and systems
-
Kang Sung-Mo, Chua Leon O. Memristive devices and systems. Proc IEEE 1976, 64(2):209-223.
-
(1976)
Proc IEEE
, vol.64
, Issue.2
, pp. 209-223
-
-
Kang, S.-M.1
Chua, L.O.2
-
62
-
-
21244443854
-
Nonlinear circuit foundations for nanodevices, Part I: the four-element torus
-
Chua L.O. Nonlinear circuit foundations for nanodevices, Part I: the four-element torus. Proc IEEE 2003, 91(11):1830-1859.
-
(2003)
Proc IEEE
, vol.91
, Issue.11
, pp. 1830-1859
-
-
Chua, L.O.1
-
63
-
-
70349668524
-
Circuits elements with memory: memristors, memcapacitors and meminductors
-
Chua Leon O., Di Ventra Massimiliano, Pershin Yuriy V Circuits elements with memory: memristors, memcapacitors and meminductors. Proc IEEE 2009, 97(10):1717-1724.
-
(2009)
Proc IEEE
, vol.97
, Issue.10
, pp. 1717-1724
-
-
Chua, L.O.1
Di Ventra, M.2
Pershin, Y.V.3
-
64
-
-
57849122145
-
How we found the missing memristor
-
Williams R.S. How we found the missing memristor. IEEE Spectrum 2008, 45(12):28-35.
-
(2008)
IEEE Spectrum
, vol.45
, Issue.12
, pp. 28-35
-
-
Williams, R.S.1
-
66
-
-
70249115683
-
Memristive model of amoeba learning
-
Di Ventra Massimiliano, Pershin Yuriy V., La Fontaine Steven Memristive model of amoeba learning. Phys Rev E 2009, 80(2):80-83.
-
(2009)
Phys Rev E
, vol.80
, Issue.2
, pp. 80-83
-
-
Di Ventra, M.1
Pershin, Y.V.2
La Fontaine, S.3
-
67
-
-
77951026760
-
Nanoscale memristor device as synapse in neuromorphic systems
-
Ebong I., Bhadviya Bhavitavya B., Mazumder P., Lu Wei, Jo Sung-Hyun, Chang Ting Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett 2010, 10:1297-1301.
-
(2010)
Nano Lett
, vol.10
, pp. 1297-1301
-
-
Ebong, I.1
Bhadviya, B.B.2
Mazumder, P.3
Lu, W.4
Jo, S.-H.5
Chang, T.6
-
68
-
-
70349668524
-
Circuits elements with memory: memristors, memcapacitors and meminductors
-
Chua L.O., Di Ventra Massimiliano, Pershin Yuriy V Circuits elements with memory: memristors, memcapacitors and meminductors. Proc IEEE 2009, 97(10):1717-1724.
-
(2009)
Proc IEEE
, vol.97
, Issue.10
, pp. 1717-1724
-
-
Chua, L.O.1
Di Ventra, M.2
Pershin, Y.V.3
-
70
-
-
84861189029
-
Port-hamiltonian formulation of systems with memory
-
Doria-Cerezo Arnau, Jeltsema Dimitri Port-hamiltonian formulation of systems with memory. Proc IEEE 2012, 100(6):1928-1937.
-
(2012)
Proc IEEE
, vol.100
, Issue.6
, pp. 1928-1937
-
-
Doria-Cerezo, A.1
Jeltsema, D.2
-
71
-
-
80054031126
-
Network transfer functions using the concept of frequency dependent negative resistance
-
Bruton L.T. Network transfer functions using the concept of frequency dependent negative resistance. IEEE Trans Circ Theory 1969, 16:406-408.
-
(1969)
IEEE Trans Circ Theory
, vol.16
, pp. 406-408
-
-
Bruton, L.T.1
-
72
-
-
0014777287
-
Novel RC-active-network synthesis using generalized immittance converters
-
Antoniou A. Novel RC-active-network synthesis using generalized immittance converters. IEEE Trans Circ Theory 1970, 17(2):212-217.
-
(1970)
IEEE Trans Circ Theory
, vol.17
, Issue.2
, pp. 212-217
-
-
Antoniou, A.1
-
73
-
-
0014739342
-
A second generation current conveyor and its applications
-
Smith K.C., Sedra A.S. A second generation current conveyor and its applications. IEEE Trans Circ Theory 1970, 17(1):132-134.
-
(1970)
IEEE Trans Circ Theory
, vol.17
, Issue.1
, pp. 132-134
-
-
Smith, K.C.1
Sedra, A.S.2
-
74
-
-
0018107075
-
Realization of frequency dependent negative resistance circuits using two capacitors and a single current conveyor
-
Soliman A.M. Realization of frequency dependent negative resistance circuits using two capacitors and a single current conveyor. IEE Proc 1978, 125(12):1336-1337.
-
(1978)
IEE Proc
, vol.125
, Issue.12
, pp. 1336-1337
-
-
Soliman, A.M.1
-
75
-
-
0022683192
-
On the realization of floating active elements
-
Senani R. On the realization of floating active elements. IEEE Trans Circ Syst 1986, 33(3):323-324.
-
(1986)
IEEE Trans Circ Syst
, vol.33
, Issue.3
, pp. 323-324
-
-
Senani, R.1
-
76
-
-
80053624133
-
Two new families of floating FDNR circuits
-
(Article ID 563761), 7 p
-
Saad Ramy A., Soliman Ahmed M. Two new families of floating FDNR circuits. J Elect Comput Eng 2010, 2010. (Article ID 563761), 7 p.
-
(2010)
J Elect Comput Eng
, vol.2010
-
-
Saad, R.A.1
Soliman, A.M.2
-
80
-
-
82155162749
-
Analogue fractional-order generalized memristive devices
-
San Diego, USA., 2009.
-
Petráš I, Coopmans C, Chen YQ. Analogue fractional-order generalized memristive devices. In: Proc. of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, San Diego, USA., 2009.
-
Proc. of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
-
-
Petráš, I.1
Coopmans, C.2
Chen, Y.Q.3
-
81
-
-
84858832205
-
Memristor and the integral quantum hall effect
-
[Original Russian Text: Rekhviashvili SSh, Potapov AA. Radiotekhnika i Elektronika 2012;57(2):207-210].
-
Rekhviashvili SSh, Potapov AA. Memristor and the integral quantum hall effect. J Commun Tech Electron 2012;57(2):189-191. [Original Russian Text: Rekhviashvili SSh, Potapov AA. Radiotekhnika i Elektronika 2012;57(2):207-210].
-
(2012)
J Commun Tech Electron
, vol.57
, Issue.2
, pp. 189-191
-
-
Rekhviashvili, S.S.H.1
Potapov, A.A.2
-
85
-
-
52349119862
-
Discretization of complex-order algorithms for control applications
-
Silva Manuel F., Barbosa Ramiro S., Tenreiro Machado J.A. Discretization of complex-order algorithms for control applications. J Vib Control 2008, 14(9-10):1349-1361.
-
(2008)
J Vib Control
, vol.14
, Issue.9-10
, pp. 1349-1361
-
-
Silva, M.F.1
Barbosa, R.S.2
Tenreiro Machado, J.A.3
-
88
-
-
84869011917
-
Complex order forced van der pol oscillator
-
doi:10.1177/1077546311429150
-
Machado JAT, Pinto Carla MA. Complex order forced van der pol oscillator. J Vib Control, doi:10.1177/1077546311429150.
-
J Vib Control
-
-
Machado, J.A.T.1
Pinto Carla, M.A.2
|