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Volumn 8, Issue , 2010, Pages

Approximate solution of time-fractional chemical engineering equations: A comparative study

Author keywords

Chemical reactor; Concentration; Fractional differential equations (FDE); Reaction

Indexed keywords

DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; NUMERICAL METHODS; PERTURBATION TECHNIQUES;

EID: 77249105162     PISSN: 21945748     EISSN: 15426580     Source Type: Journal    
DOI: 10.2202/1542-6580.2156     Document Type: Article
Times cited : (19)

References (35)
  • 1
    • 60849100198 scopus 로고    scopus 로고
    • Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model
    • Mahmood A., Parveen S., Ara A., Khan NA., "Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative model." Comm. Nonlinear Sc. Num. Simul., 2009, 14, 3309-3319.
    • (2009) Comm. Nonlinear Sc. Num. Simul. , vol.14 , pp. 3309-3319
    • Mahmood, A.1    Parveen, S.2    Ara, A.3    Khan, N.A.4
  • 2
    • 72449153908 scopus 로고    scopus 로고
    • Analytical study of navier-stokes equation with fractional orders using He's homotopy perturbation and variation iteration method
    • Khan NA., Ara A., Ali SA., Mahmood A., "Analytical study of Navier-Stokes equation with fractional orders using He's homotopy perturbation and variation iteration method." Int. J. Non-Linear Sc. & Num. Simul., 2009, 10, 1127-1134.
    • (2009) Int. J. Non-Linear Sc. & Num. Simul. , vol.10 , pp. 1127-1134
    • Khan, N.A.1    Ara, A.2    Ali, S.A.3    Mahmood, A.4
  • 3
    • 3843147199 scopus 로고    scopus 로고
    • A reliable method for the numerical solution of the kinetic problems
    • Kaya D., "A reliable method for the numerical solution of the kinetic problems." App. Math. Comp. 2004, 156, 261-270.
    • (2004) App. Math. Comp. , vol.156 , pp. 261-270
    • Kaya, D.1
  • 4
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent
    • Caputo M., "Linear models of dissipation whose Q is almost frequency independent." part II, J. Roy. Astron. Soc., 1967, 13, 529-539.
    • (1967) Part II, J. Roy. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 6
    • 0032672778 scopus 로고    scopus 로고
    • Homotopy perturbation technique
    • He JH., "Homotopy perturbation technique", Comp. Methods in App. Mech. Eng., 1999, 178, 230-235.
    • (1999) Comp. Methods in App. Mech. Eng. , vol.178 , pp. 230-235
    • He, J.H.1
  • 7
    • 0033702384 scopus 로고    scopus 로고
    • A coupling technique of homotopy technique and perturbation technique for nonlinear problems
    • He JH., "A coupling technique of homotopy technique and perturbation technique for nonlinear problems". Int. J. Nonlinear Mech. 2000, 35, 37-43.
    • (2000) Int. J. Nonlinear Mech. , vol.35 , pp. 37-43
    • He, J.H.1
  • 8
    • 4344696077 scopus 로고    scopus 로고
    • Asymptopology by homotopy perturbation method
    • He JH., "Asymptopology by homotopy perturbation method." App. Math. Comp. 2004, 156, 591-596.
    • (2004) App. Math. Comp. , vol.156 , pp. 591-596
    • He, J.H.1
  • 9
    • 33746584753 scopus 로고    scopus 로고
    • New interpretation of homotopy perturbation method
    • He JH., "New interpretation of homotopy perturbation method". Int. J. Modern Phy. B, 2006, 20, 2561-2568.
    • (2006) Int. J. Modern Phy. B , vol.20 , pp. 2561-2568
    • He, J.H.1
  • 10
    • 50949124409 scopus 로고    scopus 로고
    • New interpretation of homotopy perturbation method
    • He JH., "New interpretation of homotopy perturbation method." Topol. Methods in Nonlinear Anal. 2008, 31(2), 205-209.
    • (2008) Topol. Methods in Nonlinear Anal. , vol.31 , Issue.2 , pp. 205-209
    • He, J.H.1
  • 11
    • 1242287587 scopus 로고    scopus 로고
    • The homotopy perturbation method for nonlinear oscillators with discontinuities
    • He JH., "The homotopy perturbation method for nonlinear oscillators with discontinuities." App. Math. Comput. 2004, 151, 287-292.
    • (2004) App. Math. Comput. , vol.151 , pp. 287-292
    • He, J.H.1
  • 12
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equation
    • He JH., "Application of homotopy perturbation method to nonlinear wave equation." Chaos Solitons & Fractals 2005, 26, 695-700.
    • (2005) Chaos Solitons & Fractals , vol.26 , pp. 695-700
    • He, J.H.1
  • 13
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problem
    • He JH. "Homotopy perturbation method for solving boundary value problem." Phy. Lett. A 2006, 350, 87-98.
    • (2006) Phy. Lett. A , vol.350 , pp. 87-98
    • He, J.H.1
  • 14
    • 34250668369 scopus 로고    scopus 로고
    • Variational iteration method-Some recent results and new interpretations
    • He JH., "Variational iteration method-Some recent results and new interpretations." J. Comp. and Appl. Math. 2007, 207, 3-17.
    • (2007) J. Comp. and Appl. Math. , vol.207 , pp. 3-17
    • He, J.H.1
  • 15
    • 34748870677 scopus 로고    scopus 로고
    • Variational iteration method-new development and applications
    • He JH., Wu X-H., "Variational iteration method-New development and Applications." Comp. Math. Appl. 2007, 54, 881-894.
    • (2007) Comp. Math. Appl. , vol.54 , pp. 881-894
    • He, J.H.1    Wu, X.-H.2
  • 16
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method-A kind of non-linear analytical technique: Some examples
    • He JH., "Variational iteration method-A kind of non-linear analytical technique: Some examples." Int. J. Nonlinear Mech. 1999, 34, 4, 699-708.
    • (1999) Int. J. Nonlinear Mech. , vol.34 , Issue.4 , pp. 699-708
    • He, J.H.1
  • 17
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He JH., "Approximate analytical solution for seepage flow with fractional derivatives in porous media." Comp. Methods in Appl. Mech. & Eng. 1998, 167, 69-73.
    • (1998) Comp. Methods in Appl. Mech. & Eng. , vol.167 , pp. 69-73
    • He, J.H.1
  • 18
    • 51049089746 scopus 로고    scopus 로고
    • Variational iteration method for solving wave equation
    • Hameda AA., "Variational iteration method for solving wave equation." Comput. Math. Appl. 2008, 56, 1948-1953.
    • (2008) Comput. Math. Appl. , vol.56 , pp. 1948-1953
    • Hameda, A.A.1
  • 19
    • 34748905912 scopus 로고    scopus 로고
    • The variation iteration method: A reliable analytical tool for solving linear and nonlinear wave equations
    • Wazwaz AM., "The variation iteration method: A reliable analytical tool for solving linear and nonlinear wave equations." Computer Math. Appl. 2007, 54, 926-932.
    • (2007) Computer Math. Appl. , vol.54 , pp. 926-932
    • Wazwaz, A.M.1
  • 20
    • 34748831014 scopus 로고    scopus 로고
    • Application of he's method to nonlinear chemistry problems
    • Ganji DD., Nourollahi M., Mohseni E., "Application of He's method to nonlinear chemistry problems." Comp. Math. Appl. 2007, 54, 1122-1132.
    • (2007) Comp. Math. Appl. , vol.54 , pp. 1122-1132
    • Ganji, D.D.1    Nourollahi, M.2    Mohseni, E.3
  • 21
    • 0005354884 scopus 로고
    • The solution of a set of reaction rate equations
    • Wales (ED.), Academic Press
    • Robertson HH., "The solution of a set of reaction rate equations, in: Wales (ED.) Numerical Analysis: An Introduction." Academic Press 1966.
    • (1966) Numerical Analysis: An Introduction
    • Robertson, H.H.1
  • 22
    • 33847062377 scopus 로고    scopus 로고
    • New applications of adomian decomposition method
    • El-Wakil SA., Abdou MA., "New applications of Adomian decomposition method." Chaos Solitons and Fractals, 2007, 33, 513-522.
    • (2007) Chaos Solitons and Fractals , vol.33 , pp. 513-522
    • El-Wakil, S.A.1    Abdou, M.A.2
  • 26
    • 0020765202 scopus 로고
    • A theoretical basis for the applications of fractional calculus to viscoelasticity
    • Bagley RL., "A theoretical basis for the applications of fractional calculus to viscoelasticity", J. Rheol. 1983, 27, 201-210.
    • (1983) J. Rheol. , vol.27 , pp. 201-210
    • Bagley, R.L.1
  • 27
    • 74449084990 scopus 로고    scopus 로고
    • The variational iteration method which should be followed
    • He JH, Wu GC., Austan F., "The variational iteration method which should be followed", Nonlin. Sc. Lett. A, 2010, 1(1), 1-30.
    • (2010) Nonlin. Sc. Lett. A , vol.1 , Issue.1 , pp. 1-30
    • He, J.H.1    Wu, G.C.2    Austan, F.3
  • 28
    • 51749111612 scopus 로고    scopus 로고
    • Solution of fractional vibration equation by the variational iteration method and modified decomposition method
    • Das S., "Solution of fractional vibration equation by the variational iteration method and modified decomposition method", Int. J. Nonl. Sc. Num. Simul., 2008, 9(4), 361-366.
    • (2008) Int. J. Nonl. Sc. Num. Simul. , vol.9 , Issue.4 , pp. 361-366
    • Das, S.1
  • 30
    • 12944331178 scopus 로고    scopus 로고
    • Solution of the heldane equation for substrate inhibition enzyme kinetics using the decomposition method
    • Sonnad JR., Goudar CT., "Solution of the Heldane equation for substrate inhibition enzyme kinetics using the decomposition method", Math. Comp. Model., 2004, 40, 573-582.
    • (2004) Math. Comp. Model. , vol.40 , pp. 573-582
    • Sonnad, J.R.1    Goudar, C.T.2
  • 31
    • 0033114412 scopus 로고    scopus 로고
    • A second order scheme for the brusselator reaction-diffusion system
    • Twizell EH, Gumel, AB., Cao Q., "A second order scheme for the Brusselator reaction-diffusion system", J. Math. Chem., 1999, 26, 297-316.
    • (1999) J. Math. Chem. , vol.26 , pp. 297-316
    • Twizell, E.H.1    Gumel, A.B.2    Cao, Q.3
  • 32
    • 58349100241 scopus 로고    scopus 로고
    • Variational iteration method for a reaction-diffusion process
    • Wang S-Q., He JH., "Variational iteration method for a reaction-diffusion process", Int. J. Chem. React. Engg. 2008, 6, 1-8.
    • (2008) Int. J. Chem. React. Engg. , vol.6 , pp. 1-8
    • Wang, S.-Q.1    He, J.H.2
  • 33
    • 0010178279 scopus 로고
    • An analog simulation of non integer order transfer functions for analysis of electrode processes
    • Ichise M., Nagayanagi M., Kojima T., "An analog simulation of non integer order transfer functions for analysis of electrode processes", J. Electron. Chem. Interf. Electrochem., 1971, 33, 253-265.
    • (1971) J. Electron. Chem. Interf. Electrochem. , vol.33 , pp. 253-265
    • Ichise, M.1    Nagayanagi, M.2    Kojima, T.3
  • 34
    • 0021647967 scopus 로고
    • Application of positive reality princible to metal electrode linear polarization phenomena
    • Sun HH., Onaral B., Tsao Y., "Application of positive reality princible to metal electrode linear polarization phenomena", IEEE Trans. Bimed. Eng. 1984, 31, 664-674.
    • (1984) IEEE Trans. Bimed. Eng. , vol.31 , pp. 664-674
    • Sun, H.H.1    Onaral, B.2    Tsao, Y.3
  • 35
    • 0021424253 scopus 로고
    • Linear approximation of transfer function with a pole of fractional order
    • Sun HH., Abdelvahab AA., Onaral B., "Linear approximation of transfer function with a pole of fractional order", IEEE Trans. Automat. Control, 1984, 29, 441-444.
    • (1984) IEEE Trans. Automat. Control , vol.29 , pp. 441-444
    • Sun, H.H.1    Abdelvahab, A.A.2    Onaral, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.