-
1
-
-
0020765202
-
A theoretical basis for the application of fractional calculus to viscoelasticity
-
Bagley R.L., and Torvik P.J. A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheology 27 3 (1983) 201-210
-
(1983)
J. Rheology
, vol.27
, Issue.3
, pp. 201-210
-
-
Bagley, R.L.1
Torvik, P.J.2
-
2
-
-
0020751558
-
Fractional calculus-a different approach to the analysis of viscoelastically damped structures
-
Bagley R.L., and Torvik P.J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures. AIAA J. 21 5 (1983) 741-748
-
(1983)
AIAA J.
, vol.21
, Issue.5
, pp. 741-748
-
-
Bagley, R.L.1
Torvik, P.J.2
-
3
-
-
0022076968
-
Fractional calculus in the transient analysis of viscoelastically damped structures
-
Bagley R.L., and Torvik P.J. Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA J. 23 6 (1985) 918-925
-
(1985)
AIAA J.
, vol.23
, Issue.6
, pp. 918-925
-
-
Bagley, R.L.1
Torvik, P.J.2
-
4
-
-
0010178279
-
An analog simulation of non-integer order transfer functions for analysis of electrode processes
-
Ichise M., Nagayanagi Y., and Kojima T. An analog simulation of non-integer order transfer functions for analysis of electrode processes. J. Electronical. Chem. Interfacial Electrochem. 33 (1971) 253-265
-
(1971)
J. Electronical. Chem. Interfacial Electrochem.
, vol.33
, pp. 253-265
-
-
Ichise, M.1
Nagayanagi, Y.2
Kojima, T.3
-
5
-
-
0021647967
-
Application of positive reality principle to metal electrode linear polarization phenomena
-
Sun H.H., Onaral B., and Tsao Y. Application of positive reality principle to metal electrode linear polarization phenomena. IEEE Trans. Biomed. Eng. BME-31 10 (October 1984) 664-674
-
(1984)
IEEE Trans. Biomed. Eng.
, vol.BME-31
, Issue.10
, pp. 664-674
-
-
Sun, H.H.1
Onaral, B.2
Tsao, Y.3
-
6
-
-
0021424253
-
Linear approximation of transfer function with a pole of fractional order
-
Sun H.H., Abdelwahab A.A., and Onaral B. Linear approximation of transfer function with a pole of fractional order. IEEE Trans. Automat. Control AC-29 5 (1984) 441-444
-
(1984)
IEEE Trans. Automat. Control
, vol.AC-29
, Issue.5
, pp. 441-444
-
-
Sun, H.H.1
Abdelwahab, A.A.2
Onaral, B.3
-
7
-
-
84926570205
-
Some noises with 1/f spectrum, a bridge between direct current and white noise
-
Mandelbrot B. Some noises with 1/f spectrum, a bridge between direct current and white noise. IEEE Trans. Inform. Theory 13 2 (April 1967) 289-298
-
(1967)
IEEE Trans. Inform. Theory
, vol.13
, Issue.2
, pp. 289-298
-
-
Mandelbrot, B.1
-
8
-
-
0026124343
-
Fractional order state equations for the control of viscoelastic structures
-
Bagley R.L., and Calico R.A. Fractional order state equations for the control of viscoelastic structures. J. Guid. Control Dynam. 14 2 (March-April 1991) 304-311
-
(1991)
J. Guid. Control Dynam.
, vol.14
, Issue.2
, pp. 304-311
-
-
Bagley, R.L.1
Calico, R.A.2
-
9
-
-
0021440218
-
Application of fractional calculus to he theory of viscoelasticity
-
Koeller R.C. Application of fractional calculus to he theory of viscoelasticity. J. Appl. Mech. 51 (June 1984) 299-307
-
(1984)
J. Appl. Mech.
, vol.51
, pp. 299-307
-
-
Koeller, R.C.1
-
10
-
-
0022700808
-
Polynomial operators. Stieltjes convolution and fractional calculus in hereditary mechanics
-
Koeller R.C. Polynomial operators. Stieltjes convolution and fractional calculus in hereditary mechanics. Acta Mech. 58 (1986) 251-264
-
(1986)
Acta Mech.
, vol.58
, pp. 251-264
-
-
Koeller, R.C.1
-
13
-
-
0001983732
-
Fractional calculus: some basic problem in continuum and statistical mechanics
-
Carpinteri A., and Mainardi F. (Eds), Springer, Wein, New York
-
Mainardi F. Fractional calculus: some basic problem in continuum and statistical mechanics. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer, Wein, New York 291-348
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 291-348
-
-
Mainardi, F.1
-
14
-
-
0030867045
-
Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids
-
Rossikhin Y.A., and Shitikova M.V. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 50 (1997) 15-67
-
(1997)
Appl. Mech. Rev.
, vol.50
, pp. 15-67
-
-
Rossikhin, Y.A.1
Shitikova, M.V.2
-
15
-
-
3042776917
-
Fractional calculus in bioengineering
-
Magin R.L. Fractional calculus in bioengineering. Crit. Rev. Biomed. Eng. 32 1 (2004) 1-104
-
(2004)
Crit. Rev. Biomed. Eng.
, vol.32
, Issue.1
, pp. 1-104
-
-
Magin, R.L.1
-
16
-
-
4444254886
-
Fractional calculus in bioengineering-part 2
-
Magin R.L. Fractional calculus in bioengineering-part 2. Crit. Rev. Biomed. Eng. 32 2 (2004) 105-193
-
(2004)
Crit. Rev. Biomed. Eng.
, vol.32
, Issue.2
, pp. 105-193
-
-
Magin, R.L.1
-
17
-
-
11144305217
-
Fractional calculus in bioengineering-part 3
-
Magin R.L. Fractional calculus in bioengineering-part 3. Crit. Rev. Biomed. Eng. 32 3/4 (2004) 194-377
-
(2004)
Crit. Rev. Biomed. Eng.
, vol.32
, Issue.3-4
, pp. 194-377
-
-
Magin, R.L.1
-
19
-
-
0003598080
-
-
Gordon and Breach Science Publishers, Longhorne, PA
-
Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integrals and Derivatives-Theory and Applications (1993), Gordon and Breach Science Publishers, Longhorne, PA
-
(1993)
Fractional Integrals and Derivatives-Theory and Applications
-
-
Samko, S.G.1
Kilbas, A.A.2
Marichev, O.I.3
-
21
-
-
0002847893
-
Fractional calculus: integral and differential equations of fractional order
-
Carpinteri A., and Mainardi F. (Eds), Springer, Wein, New York
-
Gorenflo R., and Mainardi F. Fractional calculus: integral and differential equations of fractional order. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer, Wein, New York 223-276
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 223-276
-
-
Gorenflo, R.1
Mainardi, F.2
-
23
-
-
0010970550
-
Impulse response function of an oscillator with fractional derivative in damping description
-
Gaul L., Klein P., and Kempfle S. Impulse response function of an oscillator with fractional derivative in damping description. Mech. Res. Comm. 16 5 (1989) 4447-4472
-
(1989)
Mech. Res. Comm.
, vol.16
, Issue.5
, pp. 4447-4472
-
-
Gaul, L.1
Klein, P.2
Kempfle, S.3
-
25
-
-
0003001893
-
An eigenvector expansion method for the solution of motion containing fractional derivatives
-
Suarez L.E., and Shokooh A. An eigenvector expansion method for the solution of motion containing fractional derivatives. ASME. J. Appl. Mech. 64 (1997) 629-635
-
(1997)
ASME. J. Appl. Mech.
, vol.64
, pp. 629-635
-
-
Suarez, L.E.1
Shokooh, A.2
-
26
-
-
0031259296
-
Time domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations
-
Enelund M., and Josefson B.L. Time domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations. AIAA J. 35 10 (1997) 1630-1637
-
(1997)
AIAA J.
, vol.35
, Issue.10
, pp. 1630-1637
-
-
Enelund, M.1
Josefson, B.L.2
-
27
-
-
0033097283
-
Damping described by fading memory-analysis and application to fractional derivative models
-
Enelund M., and Lesieutre G.A. Damping described by fading memory-analysis and application to fractional derivative models. Internat. J. Solid Structures 36 29 (1999) 939-970
-
(1999)
Internat. J. Solid Structures
, vol.36
, Issue.29
, pp. 939-970
-
-
Enelund, M.1
Lesieutre, G.A.2
-
28
-
-
0033097283
-
Time domain modeling of damping using anelastic displacement fields and fractional calculus
-
Enelund M., and Olsson P. Time domain modeling of damping using anelastic displacement fields and fractional calculus. Internat. J. Solids Structures 36 6 (1999) 939-970
-
(1999)
Internat. J. Solids Structures
, vol.36
, Issue.6
, pp. 939-970
-
-
Enelund, M.1
Olsson, P.2
-
29
-
-
0002847893
-
Fractional calculus: some numerical methods
-
Carpinteri A., and Mainardi F. (Eds), Springer, Wein, New York
-
Gorenflo R. Fractional calculus: some numerical methods. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer, Wein, New York 277-290
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 277-290
-
-
Gorenflo, R.1
-
30
-
-
0025387251
-
Application of fractional derivatives to seismic analysis of base-isolated models
-
Koh C.G., and Kelly J.M. Application of fractional derivatives to seismic analysis of base-isolated models. Earthquake Eng. Structural Dynamics 19 (1990) 229-241
-
(1990)
Earthquake Eng. Structural Dynamics
, vol.19
, pp. 229-241
-
-
Koh, C.G.1
Kelly, J.M.2
-
31
-
-
34250103892
-
Computational algorithms and finite element formulation involving fractional operators
-
Padovan J. Computational algorithms and finite element formulation involving fractional operators. Comput. Mech. 2 (1987) 271-287
-
(1987)
Comput. Mech.
, vol.2
, pp. 271-287
-
-
Padovan, J.1
-
32
-
-
33745687339
-
-
P. Ruge, N. Wagner, Time-domain solutions for vibration systems with feding memory, European Conference of Computational Mechanics, Munchen, Germany, August 31-September 3, 1999.
-
-
-
-
33
-
-
0033471671
-
A comparison of numerical methods in applied to a fractional model of damping
-
Shokooh A., and Suarez L.E. A comparison of numerical methods in applied to a fractional model of damping. J. Vibration Controls 5 (1999) 331-354
-
(1999)
J. Vibration Controls
, vol.5
, pp. 331-354
-
-
Shokooh, A.1
Suarez, L.E.2
-
34
-
-
0036554885
-
A numerical scheme for dynamic systems containing fractional derivatives
-
Yuan L., and Agrawal O.P. A numerical scheme for dynamic systems containing fractional derivatives. Trans. ASME. J. Vibration and Acoustics 124 (2002) 321-324
-
(2002)
Trans. ASME. J. Vibration and Acoustics
, vol.124
, pp. 321-324
-
-
Yuan, L.1
Agrawal, O.P.2
-
35
-
-
0036650479
-
A predictor-corrector approach for the numerical solution of fractional differential equations
-
Diethelm K., Ford N.J., and Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 29 1-4 (2002) 3-22
-
(2002)
Nonlinear Dynamics
, vol.29
, Issue.1-4
, pp. 3-22
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
37
-
-
33745701558
-
-
P. Kumar, O.P. Agrawal, A cubic scheme for numerical solution of fractional differential equations, in: Proceedings of the Fifth EUROMECH Nonlinear Dynamics Conference, ENOC-2005, pp. 1479-1487.
-
-
-
-
39
-
-
0031337669
-
Applications and numerical analysis of partial differential Volterra equations: a brief survey
-
Shaw S., and Whiteman J.R. Applications and numerical analysis of partial differential Volterra equations: a brief survey. Comput. Method Appl. Mech. Eng. 150 (1997) 397-409
-
(1997)
Comput. Method Appl. Mech. Eng.
, vol.150
, pp. 397-409
-
-
Shaw, S.1
Whiteman, J.R.2
-
40
-
-
0348158242
-
m E methods
-
m E methods. Computing 71 (2003) 305-319
-
(2003)
Computing
, vol.71
, pp. 305-319
-
-
Diethelm, K.1
-
41
-
-
3042709180
-
Multi-order fractional differential equations and their numerical solution
-
Diethelm K., and Ford N.J. Multi-order fractional differential equations and their numerical solution. Appl. Math. Comput. 154 3 (2004) 621-640
-
(2004)
Appl. Math. Comput.
, vol.154
, Issue.3
, pp. 621-640
-
-
Diethelm, K.1
Ford, N.J.2
-
42
-
-
0037081673
-
Analysis of fractional differential equations
-
Diethelm K., and Ford N.J. Analysis of fractional differential equations. J. Math. Anal. Appl. 265 (2002) 229-248
-
(2002)
J. Math. Anal. Appl.
, vol.265
, pp. 229-248
-
-
Diethelm, K.1
Ford, N.J.2
-
43
-
-
0037113861
-
The numerical solution of linear multi-term fractional differential equations: systems of equations
-
Edwards J.T., Ford N.J., and Simpson C.A. The numerical solution of linear multi-term fractional differential equations: systems of equations. J. Comput. Appl. Math. 148 2 (2002) 401-418
-
(2002)
J. Comput. Appl. Math.
, vol.148
, Issue.2
, pp. 401-418
-
-
Edwards, J.T.1
Ford, N.J.2
Simpson, C.A.3
-
44
-
-
33745701557
-
-
N.J. Ford, C.A. Simpson, The approximate solution of fractional differential equations of order greater than 1, Internet download, URL 〈http://www.chester.ac.uk/maths/nevillepub.html〉 May 2003.
-
-
-
-
45
-
-
33244494442
-
-
P. Kumar, O.P. Agrawal, Numerical scheme for the solution of fractional differential equations, in: Proceedings of the 2005 ASME Design Engineering Technical Conferences and Computer and Information Engineering Conference, Long Beach, California, September 24-28, 2005.
-
-
-
-
46
-
-
0002935511
-
An introduction to fractional calculus
-
Hilfer R. (Ed), World Scientific, New Jersey
-
Butzer P.L., and Westphil U. An introduction to fractional calculus. In: Hilfer R. (Ed). Applications of Fractional Calculus in Physics (2000), World Scientific, New Jersey 1-85
-
(2000)
Applications of Fractional Calculus in Physics
, pp. 1-85
-
-
Butzer, P.L.1
Westphil, U.2
-
48
-
-
33244491922
-
-
B.N. Achar, C.F. Lorenzo, T.T. Hartley, Initialization issue of the Caputo fractional derivative, in: Proceedings of the 2005 ASME Design Engineering Technical Conferences and Computer and Information Engineering Conference, Long Beach, California, September 24-28, 2005.
-
-
-
|