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Volumn 72, Issue 2, 2005, Pages 290-295

Analytical solution of a dynamic system containing fractional derivative of order one-half by adomian decomposition method

Author keywords

[No Author keywords available]

Indexed keywords

DAMPING; DECOMPOSITION; DIFFERENTIAL EQUATIONS; ELECTROCHEMISTRY; ELECTROMAGNETIC WAVES; FOURIER TRANSFORMS; RELAXATION PROCESSES; VISCOELASTICITY;

EID: 17444364074     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1839184     Document Type: Article
Times cited : (67)

References (54)
  • 4
    • 0001618393 scopus 로고    scopus 로고
    • An algorithm for the numerical solution of differential equations of fractional order
    • Diethelm, K., 1997, "An Algorithm for the Numerical Solution of Differential Equations of Fractional Order," Elec. Transact. Numer. Anal., 5, pp. 1-6.
    • (1997) Elec. Transact. Numer. Anal. , vol.5 , pp. 1-6
    • Diethelm, K.1
  • 5
    • 0010186169 scopus 로고    scopus 로고
    • The FracPECE subroutine for the numerical solution of differential equations of fractional order
    • No. 52 in GWDG-Berichte, S. Heinzel and T. Plesser, eds., Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen
    • Diethelm, K., and Freed, A. D., 1999, "The FracPECE Subroutine for the Numerical Solution of Differential Equations of Fractional Order," No. 52 in GWDG-Berichte, Forschung und wissenschaftliches Rechnen: Beiträge zum Heinz-Billing-Preis 1998, S. Heinzel and T. Plesser, eds., Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen, pp. 57-71.
    • (1999) Forschung Und Wissenschaftliches Rechnen: Beiträge zum Heinz-Billing-Preis 1998 , pp. 57-71
    • Diethelm, K.1    Freed, A.D.2
  • 6
    • 0037081673 scopus 로고    scopus 로고
    • Analysis of fractional differential equations
    • Diethelm, K., and Ford, N. J., 2002, "Analysis of Fractional Differential Equations," J. Math. Anal. Appl., 265, pp. 229-248.
    • (2002) J. Math. Anal. Appl. , vol.265 , pp. 229-248
    • Diethelm, K.1    Ford, N.J.2
  • 7
    • 0036650479 scopus 로고    scopus 로고
    • A predictor-corrector approach for the numerical solution of fractional differential equations
    • Diethelm, K., Ford, N. J., and Freed, A. D., 2002, "A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations," Nonlinear Dyn., 29, pp. 3-22.
    • (2002) Nonlinear Dyn. , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 8
    • 0012899160 scopus 로고    scopus 로고
    • Numerical solution of the bagley-torvik equation
    • Diethelm, K., and Ford, N. J., 2002, "Numerical Solution of the Bagley-Torvik Equation," Bit Numer. Math., 42(3), pp. 490-507.
    • (2002) Bit Numer. Math. , vol.42 , Issue.3 , pp. 490-507
    • Diethelm, K.1    Ford, N.J.2
  • 9
    • 0002795136 scopus 로고    scopus 로고
    • On the solution of nonlinear fractional-order differential equations used in the modeling of viscoplasticity
    • F. Keil, W. Mackens, H. Voß, and J. Werther, eds., Springer-Verlag, Heidelberg
    • Diethelm, K., and Ford, A. D., 1999, "On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity," Scientific Computing in Chemical Engineering II. Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties, F. Keil, W. Mackens, H. Voß, and J. Werther, eds., Springer-Verlag, Heidelberg, pp. 217-224.
    • (1999) Scientific Computing in Chemical Engineering II. Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties , pp. 217-224
    • Diethelm, K.1    Ford, A.D.2
  • 10
    • 0012899161 scopus 로고    scopus 로고
    • The numerical solution of linear and nonlinear fractional differential equations involving fractional derivatives of several orders
    • Manchester Center for Computational Mathematics, Manchester, England
    • Diethelm, K., and Ford, N. J., 2001, "The Numerical Solution of Linear and Nonlinear Fractional Differential Equations Involving Fractional Derivatives of Several Orders," Numerical Analysis Report No. 379, Manchester Center for Computational Mathematics, Manchester, England.
    • (2001) Numerical Analysis Report No. 379 , vol.379
    • Diethelm, K.1    Ford, N.J.2
  • 11
    • 0020765202 scopus 로고
    • A theoretical basis for the application of fractional calculus to viscoelasticity
    • Bagley, R. L., and Torvik, P. J., 1983, "A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity," J. Rheol., 27(3), pp. 201-210.
    • (1983) J. Rheol. , vol.27 , Issue.3 , pp. 201-210
    • Bagley, R.L.1    Torvik, P.J.2
  • 12
    • 0020751558 scopus 로고
    • Fractional calculus-a different approach to the analysis viscoelastically damped structures
    • Bagley, R. L., and Torvik, P. J., 1983, "Fractional Calculus-A Different Approach to the Analysis Viscoelastically Damped Structures," AIAA J., 21(5), pp. 741-748.
    • (1983) AIAA J. , vol.21 , Issue.5 , pp. 741-748
    • Bagley, R.L.1    Torvik, P.J.2
  • 13
    • 0022076968 scopus 로고
    • Fractional calculus in the transient analysis of viscoelastically damped structures
    • Bagley, R. L., and Torvik, P. J., 1985, "Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures," AIAA J., 23(6), pp. 918-925.
    • (1985) AIAA J. , vol.23 , Issue.6 , pp. 918-925
    • Bagley, R.L.1    Torvik, P.J.2
  • 14
    • 0021440218 scopus 로고
    • Application of fractional calculus to the theory of viscoelasticity
    • Koeller, R. C., 1984, "Application of Fractional Calculus to the Theory of Viscoelasticity," ASME J. Appl. Mech., 51, pp. 299-307.
    • (1984) ASME J. Appl. Mech. , vol.51 , pp. 299-307
    • Koeller, R.C.1
  • 16
    • 0026219915 scopus 로고
    • Fractional derivative maxwell model for viscous dampers
    • Makris, N., and Constaninou, M. C., 1991, "Fractional Derivative Maxwell Model for Viscous Dampers," J. Struct. Eng., 117(9), pp. 2708-2724.
    • (1991) J. Struct. Eng. , vol.117 , Issue.9 , pp. 2708-2724
    • Makris, N.1    Constaninou, M.C.2
  • 17
    • 0000400568 scopus 로고
    • Modeling of viscoelastic dampers for structural applications
    • Shen, K. L., and Soong, T. T., 1995, "Modeling of Viscoelastic Dampers for Structural Applications," J. Eng. Mech., 121, pp. 694-701.
    • (1995) J. Eng. Mech. , vol.121 , pp. 694-701
    • Shen, K.L.1    Soong, T.T.2
  • 18
    • 0030575463 scopus 로고    scopus 로고
    • Analysis of four-parameter fractional derivative model of real solid materials
    • Pritz, T., 1996, "Analysis of Four-Parameter Fractional Derivative Model of Real Solid Materials," J. Sound Vib., 195, pp. 103-115.
    • (1996) J. Sound Vib. , vol.195 , pp. 103-115
    • Pritz, T.1
  • 19
    • 0031191268 scopus 로고    scopus 로고
    • Visco-hyperelastic model for filled rubbers used in vibration isolation
    • Papoulia, K. D., and Kelly, J. M., 1997, "Visco-Hyperelastic Model for Filled Rubbers Used in Vibration Isolation," ASME J. Eng. Mater. Technol., 119, pp. 292-297.
    • (1997) ASME J. Eng. Mater. Technol. , vol.119 , pp. 292-297
    • Papoulia, K.D.1    Kelly, J.M.2
  • 20
    • 4043156890 scopus 로고
    • On the fractional derivative modeling of damping materials
    • presented for NASA Langley, College of Engineering, University of Puerto Rica, Mayaguez, PR
    • Shokooh, A., and Suarez, L., 1994, "On the Fractional Derivative Modeling of Damping Materials," Technical Report presented for NASA Langley, College of Engineering, University of Puerto Rica, Mayaguez, PR.
    • (1994) Technical Report
    • Shokooh, A.1    Suarez, L.2
  • 21
    • 24244455970 scopus 로고
    • Response of systems with damping materials modeled using fractional calculus
    • Suarez, L. E., and Shokooh, A., 1995, "Response of Systems With Damping Materials Modeled Using Fractional Calculus," ASME J. Appl. Mech. Rev., 48(11), Part 2, pp. S118-S127.
    • (1995) ASME J. Appl. Mech. Rev. , vol.48 , Issue.11 PART 2
    • Suarez, L.E.1    Shokooh, A.2
  • 22
    • 17444376571 scopus 로고
    • Finite element analysis of damping materials modeled by the fractional derivative method
    • presented for NASA Langley, College of Engineering, University of Puerto Rico, Mayaguez, PR
    • Suarez, L., Shokooh, A., and Arroyo, J., 1995, "Finite Element Analysis of Damping Materials Modeled by the Fractional Derivative Method, " Technical Report presented for NASA Langley, College of Engineering, University of Puerto Rico, Mayaguez, PR.
    • (1995) Technical Report
    • Suarez, L.1    Shokooh, A.2    Arroyo, J.3
  • 23
    • 0010970550 scopus 로고
    • Impulse response function of an oscillator with fractional derivative in damping description
    • Gaul, L., Klein, P., and Kemple, S., 1989, "Impulse Response Function of an Oscillator With Fractional Derivative in Damping Description," Mech. Res. Commun., 16(5), pp. 297-305.
    • (1989) Mech. Res. Commun. , vol.16 , Issue.5 , pp. 297-305
    • Gaul, L.1    Klein, P.2    Kemple, S.3
  • 24
    • 44949282247 scopus 로고
    • Damping description involving fractional operators
    • Gaul, L., Klein, P., and Kemple, S., 1991, "Damping Description Involving Fractional Operators," Mech. Syst. Signal Process., 5(2), pp. 8-88.
    • (1991) Mech. Syst. Signal Process. , vol.5 , Issue.2 , pp. 8-88
    • Gaul, L.1    Klein, P.2    Kemple, S.3
  • 25
    • 0025387251 scopus 로고
    • Application of fractional derivatives to seismic analysis of base-isolated models
    • Koh, C. G., and Kelly, J. M., 1990, "Application of Fractional Derivatives to Seismic Analysis of Base-Isolated Models," Earthquake Eng. Struct. Dyn., 19, pp. 229-241.
    • (1990) Earthquake Eng. Struct. Dyn. , vol.19 , pp. 229-241
    • Koh, C.G.1    Kelly, J.M.2
  • 26
    • 34250103892 scopus 로고
    • Computational algorithms for finite element formulation involving fractional operators
    • Padovan, J., 1987, "Computational Algorithms for Finite Element Formulation Involving Fractional Operators," Comput. Mech., 2, pp. 271-287.
    • (1987) Comput. Mech. , vol.2 , pp. 271-287
    • Padovan, J.1
  • 27
    • 0003001893 scopus 로고    scopus 로고
    • An eigenvector expansion method for the solution of motion containing fractional derivatives
    • Suarez, L. E., and Shokooh, A., 1997, "An Eigenvector Expansion Method for the Solution of Motion Containing Fractional Derivatives," ASME J. Appl. Mech., 64, pp. 629-635.
    • (1997) ASME J. Appl. Mech. , vol.64 , pp. 629-635
    • Suarez, L.E.1    Shokooh, A.2
  • 30
    • 0002132894 scopus 로고
    • An analytical solution of the stochastic navier-stokes system
    • Adomian, G., 1991, "An Analytical Solution of the Stochastic Navier-Stokes System," Found. Phys., 21(7), pp. 831-843.
    • (1991) Found. Phys. , vol.21 , Issue.7 , pp. 831-843
    • Adomian, G.1
  • 31
    • 17444425874 scopus 로고
    • Linear and nonlinear schrödinger equations
    • Adomian, G., and Rach, R., 1991, "Linear and Nonlinear Schrödinger Equations," Found. Phys., 21, pp. 983-991.
    • (1991) Found. Phys. , vol.21 , pp. 983-991
    • Adomian, G.1    Rach, R.2
  • 32
    • 0000244996 scopus 로고
    • Solution of physical problems by decomposition
    • Adomian, G., 1994, "Solution of Physical Problems by Decomposition," Comput. Math. Appl., 27, Nos. 9/10, pp. 145-154.
    • (1994) Comput. Math. Appl. , vol.27 , Issue.9-10 , pp. 145-154
    • Adomian, G.1
  • 33
    • 0001422946 scopus 로고    scopus 로고
    • Solutions of nonlinear P.D.E.
    • Adomian, G., 1998, "Solutions of Nonlinear P.D.E.," Appl. Math. Lett., 11(3), pp. 121-123.
    • (1998) Appl. Math. Lett. , vol.11 , Issue.3 , pp. 121-123
    • Adomian, G.1
  • 34
    • 0033241451 scopus 로고    scopus 로고
    • The decomposition method applied to the cauchy problem
    • Abbaoui, K., and Cherruault, Y., 1999, "The Decomposition Method Applied to the Cauchy Problem," Kybemetes, 28(1), pp. 68-74.
    • (1999) Kybemetes , vol.28 , Issue.1 , pp. 68-74
    • Abbaoui, K.1    Cherruault, Y.2
  • 35
    • 0037107899 scopus 로고    scopus 로고
    • A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations
    • Kaya, D., and Yokus, A., 2002, "A Numerical Comparison of Partial Solutions in the Decomposition Method for Linear and Nonlinear Partial Differential Equations," Math. Comput. Simul., 60(6), pp. 507-512.
    • (2002) Math. Comput. Simul. , vol.60 , Issue.6 , pp. 507-512
    • Kaya, D.1    Yokus, A.2
  • 36
    • 0040313517 scopus 로고    scopus 로고
    • A reliable modification of adomian decomposition method
    • Wazwaz, A., 1999, "A Reliable Modification of Adomian Decomposition Method," Appl. Math. Comput., 102(1), pp. 77-86.
    • (1999) Appl. Math. Comput. , vol.102 , Issue.1 , pp. 77-86
    • Wazwaz, A.1
  • 37
    • 0037424857 scopus 로고    scopus 로고
    • On a generalized fifth order KdV equations
    • Kaya, D., and El-Sayed, S. M., 2003, "On a Generalized Fifth Order KdV Equations," Phys. Lett. A, 310(1), pp. 44-51.
    • (2003) Phys. Lett. A , vol.310 , Issue.1 , pp. 44-51
    • Kaya, D.1    El-Sayed, S.M.2
  • 38
    • 0037411749 scopus 로고    scopus 로고
    • An application of the decomposition method for the generalized KdV and RLW equations
    • Kaya, D., and El-Sayed, S. M., 2003, "An Application of the Decomposition Method for the Generalized KdV and RLW Equations," Chaos, Solitons, Fractals, , 17(5), pp. 869-877.
    • (2003) Chaos, Solitons, Fractals , vol.17 , Issue.5 , pp. 869-877
    • Kaya, D.1    El-Sayed, S.M.2
  • 39
    • 0038112095 scopus 로고    scopus 로고
    • An explicit and numerical solutions of some fifth-order KdV equation by decomposition method
    • Kaya, D., 2003, "An Explicit and Numerical Solutions of Some Fifth-Order KdV Equation by Decomposition Method," Appl. Math. Comput., 144(2/3), pp. 353-363.
    • (2003) Appl. Math. Comput. , vol.144 , Issue.2-3 , pp. 353-363
    • Kaya, D.1
  • 40
    • 0346497913 scopus 로고    scopus 로고
    • A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation
    • Kaya, D., 2004, "A Numerical Simulation of Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation," Appl. Math. Comput., 149(3), pp. 833-841.
    • (2004) Appl. Math. Comput. , vol.149 , Issue.3 , pp. 833-841
    • Kaya, D.1
  • 41
    • 17444419514 scopus 로고
    • The adomian method applied to some extraordinary differential equations
    • George, A. J., and Chakrabarti, A., 1995, "The Adomian Method Applied to Some Extraordinary Differential Equations," Appl. Math. Lett., 8(3), pp. 91-97.
    • (1995) Appl. Math. Lett. , vol.8 , Issue.3 , pp. 91-97
    • George, A.J.1    Chakrabarti, A.2
  • 42
    • 0012820367 scopus 로고
    • Solutions of non-integer order differential equations via the adomian decomposition method
    • Arora, H. L., and Abdelwahid, F. I., 1993, "Solutions of Non-Integer Order Differential Equations Via the Adomian Decomposition Method," Appl. Math. Lett., 6(1), pp. 21-23.
    • (1993) Appl. Math. Lett. , vol.6 , Issue.1 , pp. 21-23
    • Arora, H.L.1    Abdelwahid, F.I.2
  • 43
    • 0009867678 scopus 로고    scopus 로고
    • The decomposition method for fractional differential equations
    • Shawagfeh, N. T., 1999, "The Decomposition Method for Fractional Differential Equations," J. Fractional Calculus, 16, pp. 27-33.
    • (1999) J. Fractional Calculus , vol.16 , pp. 27-33
    • Shawagfeh, N.T.1
  • 44
    • 0037174280 scopus 로고    scopus 로고
    • Analytical approximate solutions for nonlinear fractional differential equations
    • Shawagfeh, N. T., 2002, "Analytical Approximate Solutions for Nonlinear Fractional Differential Equations," Appl. Math. Comput., 131, pp. 517-529.
    • (2002) Appl. Math. Comput. , vol.131 , pp. 517-529
    • Shawagfeh, N.T.1
  • 45
    • 17444386836 scopus 로고    scopus 로고
    • Solution of an extraordinary differential equation by adomian decomposition method
    • Saha Ray, S., and Bera, R. K., 2004, "Solution of an Extraordinary Differential Equation by Adomian Decomposition Method," J. Appl. Math., 4, pp. 331-338.
    • (2004) J. Appl. Math. , vol.4 , pp. 331-338
    • Saha Ray, S.1    Bera, R.K.2
  • 46
    • 0030187555 scopus 로고    scopus 로고
    • Adomian's polynomials for nonlinear operators
    • Seng, V., Abbaoui, K., and Cherruault, Y., 1996, "Adomian's Polynomials for Nonlinear Operators," Math. Comput. Modell., 24(1), pp. 59-65.
    • (1996) Math. Comput. Modell. , vol.24 , Issue.1 , pp. 59-65
    • Seng, V.1    Abbaoui, K.2    Cherruault, Y.3
  • 47
    • 0037420925 scopus 로고    scopus 로고
    • A mathematical model of adomian polynomials
    • Abdelwahid, F., 2003, "A Mathematical Model of Adomian Polynomials," Appl. Math. Comput., 141, pp. 447-453.
    • (2003) Appl. Math. Comput. , vol.141 , pp. 447-453
    • Abdelwahid, F.1
  • 48
    • 84970868898 scopus 로고
    • Convergence of adomian's method
    • Cherruault, Y., 1989, "Convergence of Adomian's Method," Kybernetes, 18(2), pp. 31-38.
    • (1989) Kybernetes , vol.18 , Issue.2 , pp. 31-38
    • Cherruault, Y.1
  • 49
    • 43949159125 scopus 로고
    • Convergence of adomian's method applied to differential equations
    • Abbaoui, K., and Cherruault, Y., 1994, "Convergence of Adomian's Method Applied to Differential Equations," Comput. Math. Appl., 28(5), pp. 103-109.
    • (1994) Comput. Math. Appl. , vol.28 , Issue.5 , pp. 103-109
    • Abbaoui, K.1    Cherruault, Y.2
  • 50
    • 0000487641 scopus 로고
    • New ideas for proving convergence of decomposition methods
    • Abbaoui, K., and Cherruault, Y., 1995, "New Ideas for Proving Convergence of Decomposition Methods," Comput. Math. Appl., 29, pp. 103-108.
    • (1995) Comput. Math. Appl. , vol.29 , pp. 103-108
    • Abbaoui, K.1    Cherruault, Y.2
  • 51
    • 0033240054 scopus 로고    scopus 로고
    • New results of convergence of adomian's method
    • Himoun, N., Abbaoui, K., and Cherruault, Y., 1999, "New Results of Convergence of Adomian's Method," Kybemetes, 28(4), pp. 423-429.
    • (1999) Kybemetes , vol.28 , Issue.4 , pp. 423-429
    • Himoun, N.1    Abbaoui, K.2    Cherruault, Y.3
  • 53
    • 0001452371 scopus 로고    scopus 로고
    • Initialised fractional calculus
    • Lorenzo, C. F., and Hartley, T. T., 2000, "Initialised Fractional Calculus," Int. J. Appl. Math., 3(3), pp. 249-265.
    • (2000) Int. J. Appl. Math. , vol.3 , Issue.3 , pp. 249-265
    • Lorenzo, C.F.1    Hartley, T.T.2


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