메뉴 건너뛰기




Volumn 35, Issue 4, 2011, Pages 1937-1945

Homotopy perturbation method to space-time fractional solidification in a finite slab

Author keywords

Approximate analytical solution; Fractional heat conduction equation; Homotopy perturbation method; Moving boundary; Taylor's series

Indexed keywords

APPROXIMATE ANALYTICAL SOLUTIONS; FRACTIONAL HEAT CONDUCTION EQUATION; HOMOTOPY PERTURBATION METHOD; MOVING BOUNDARIES; TAYLOR'S SERIES;

EID: 78650286067     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.11.005     Document Type: Article
Times cited : (39)

References (38)
  • 2
    • 77953683696 scopus 로고    scopus 로고
    • NATO Public Diplomacy Division, F. Khanna, D. Matrasulov (Eds.)
    • Non-Linear Dynamics and Fundamental Interactions 2006, NATO Public Diplomacy Division. F. Khanna, D. Matrasulov (Eds.).
    • (2006) Non-Linear Dynamics and Fundamental Interactions
  • 3
    • 3543083566 scopus 로고    scopus 로고
    • Anomalous heat conduction and anomalous diffusion in one-dimensional systems
    • Li B., Wang J. Anomalous heat conduction and anomalous diffusion in one-dimensional systems. Phys. Rev. Lett. 2003, 91:044301.
    • (2003) Phys. Rev. Lett. , vol.91 , pp. 044301
    • Li, B.1    Wang, J.2
  • 4
    • 85038286906 scopus 로고    scopus 로고
    • Li and Wang Reply
    • Li B., Wang J. Li and Wang Reply. Phys. Rev. Lett. 2004, 92:089402.
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 089402
    • Li, B.1    Wang, J.2
  • 5
    • 13844253772 scopus 로고    scopus 로고
    • Fractional heat conduction equation and associated thermal stress
    • Povstenko Y.Z. Fractional heat conduction equation and associated thermal stress. J. Therm. Stresses 2005, 28:83-102.
    • (2005) J. Therm. Stresses , vol.28 , pp. 83-102
    • Povstenko, Y.Z.1
  • 6
    • 77953685231 scopus 로고    scopus 로고
    • The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems
    • Jiang X., Xu M. The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems. Physica A 2010, 389:3368-3374.
    • (2010) Physica A , vol.389 , pp. 3368-3374
    • Jiang, X.1    Xu, M.2
  • 7
    • 35248884030 scopus 로고    scopus 로고
    • Homotopy Perturbation method for fractional K dV-Burgers equation
    • Wang Q. Homotopy Perturbation method for fractional K dV-Burgers equation. Chaos soliton Fract. 2008, 35:843-850.
    • (2008) Chaos soliton Fract. , vol.35 , pp. 843-850
    • Wang, Q.1
  • 9
    • 0024139481 scopus 로고    scopus 로고
    • Free boundary problems in controlled release pharmaceuticals: II. swelling-controlled release
    • Cohen D.S., Erneux T. Free boundary problems in controlled release pharmaceuticals: II. swelling-controlled release. SIAM J. Appl. Math. 2005, 48:1186-1194.
    • (2005) SIAM J. Appl. Math. , vol.48 , pp. 1186-1194
    • Cohen, D.S.1    Erneux, T.2
  • 10
    • 13644249177 scopus 로고    scopus 로고
    • Swelling controlled release of drug in spherical polymer-penetrant Systems
    • Lin J.S., Peng Y.-L. Swelling controlled release of drug in spherical polymer-penetrant Systems. Int. J. Heat Mass Transfer. 2005, 48:1186-1194.
    • (2005) Int. J. Heat Mass Transfer. , vol.48 , pp. 1186-1194
    • Lin, J.S.1    Peng, Y.-L.2
  • 12
    • 0030176475 scopus 로고    scopus 로고
    • Diffusional release of a dispersed solute from a spherical polymer matrix
    • Abdekhodaie M.J., Cheng Y.-L. Diffusional release of a dispersed solute from a spherical polymer matrix. J. Memb. Sci. 1996, 115:171-178.
    • (1996) J. Memb. Sci. , vol.115 , pp. 171-178
    • Abdekhodaie, M.J.1    Cheng, Y.-L.2
  • 13
    • 0031060456 scopus 로고    scopus 로고
    • Diffusional release of a dispersed solute from planar and spherical matrices into finite external volume
    • Abdekhodate M.J., Cheng Y.-L. Diffusional release of a dispersed solute from planar and spherical matrices into finite external volume. J. Contr. Release. 1997, 43:175-182.
    • (1997) J. Contr. Release. , vol.43 , pp. 175-182
    • Abdekhodate, M.J.1    Cheng, Y.-L.2
  • 14
    • 77955895114 scopus 로고    scopus 로고
    • Heat-balance integral to fractional (half-time)
    • Hristov J. Heat-balance integral to fractional (half-time). Heat Diffus. Sub-Model Therm. Sci. 2010, 14:291-316.
    • (2010) Heat Diffus. Sub-Model Therm. Sci. , vol.14 , pp. 291-316
    • Hristov, J.1
  • 17
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of a homotopy technique and a perturbation technique for Non-linear problems
    • He J. A coupling method of a homotopy technique and a perturbation technique for Non-linear problems. Int. J. Non-linear Mech. 2000, 35:37-43.
    • (2000) Int. J. Non-linear Mech. , vol.35 , pp. 37-43
    • He, J.1
  • 18
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: a new nonlinear analytical technique
    • He J. Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 2003, 135:73-79.
    • (2003) Appl. Math. Comput. , vol.135 , pp. 73-79
    • He, J.1
  • 19
    • 1242287587 scopus 로고    scopus 로고
    • Homotopy perturbation method for nonlinear oscillators with discontinuities
    • He J. Homotopy perturbation method for nonlinear oscillators with discontinuities. Appl. Math. Comput. 2004, 151:287-292.
    • (2004) Appl. Math. Comput. , vol.151 , pp. 287-292
    • He, J.1
  • 20
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problems
    • He J. Homotopy perturbation method for solving boundary value problems. Phys. lett. A. 2006, 350:87-88.
    • (2006) Phys. lett. A. , vol.350 , pp. 87-88
    • He, J.1
  • 21
    • 0034447514 scopus 로고    scopus 로고
    • A modified perturbation technique depending upon an artificial parameter
    • He J. A modified perturbation technique depending upon an artificial parameter. Meccanica 2000, 35:299-311.
    • (2000) Meccanica , vol.35 , pp. 299-311
    • He, J.1
  • 22
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He J. Application of homotopy perturbation method to nonlinear wave equations. chaos soliton Fract. 2005, 26:695-700.
    • (2005) chaos soliton Fract. , vol.26 , pp. 695-700
    • He, J.1
  • 23
    • 78650267004 scopus 로고    scopus 로고
    • Non-Perturbative Methods for strongly nonlinear problems, Dissertation, de-Verlag im Internet GmbH, Berlin,
    • J. He, Non-Perturbative Methods for strongly nonlinear problems, Dissertation, de-Verlag im Internet GmbH, Berlin, 2006.
    • (2006)
    • He, J.1
  • 24
    • 33746584753 scopus 로고    scopus 로고
    • New interpretation of homotopy perturbation method
    • He J. New interpretation of homotopy perturbation method. Int. J. Modern Phys. B 2006, 20:1-7.
    • (2006) Int. J. Modern Phys. B , vol.20 , pp. 1-7
    • He, J.1
  • 25
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J. Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B 2006, 20:1141-1199.
    • (2006) Int. J. Modern Phys. B , vol.20 , pp. 1141-1199
    • He, J.1
  • 26
    • 35348869861 scopus 로고    scopus 로고
    • Modified homotopy perturbation method:Application to quadratic Riccati differential equation of fractional order
    • Odibat Z., Momani S. Modified homotopy perturbation method:Application to quadratic Riccati differential equation of fractional order. chaos soliton fract. 2008, 36:167-174.
    • (2008) chaos soliton fract. , vol.36 , pp. 167-174
    • Odibat, Z.1    Momani, S.2
  • 27
    • 34247395044 scopus 로고    scopus 로고
    • Homotopy perturbation method for nonlinear partial differential equations of fractional order
    • Momani S., Odibat Z. Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys. Lett. A 2007, 365:345-350.
    • (2007) Phys. Lett. A , vol.365 , pp. 345-350
    • Momani, S.1    Odibat, Z.2
  • 28
    • 35248884030 scopus 로고    scopus 로고
    • Homotopy Perturbation method for fractional KdV-Burgers equation
    • Wang Q. Homotopy Perturbation method for fractional KdV-Burgers equation. Chaos soliton Fract. 2008, 35:843-850.
    • (2008) Chaos soliton Fract. , vol.35 , pp. 843-850
    • Wang, Q.1
  • 29
    • 34250643564 scopus 로고    scopus 로고
    • Homotopy perturbation method for fractional K dV equation
    • Wang Q. Homotopy perturbation method for fractional K dV equation. Appl. Math. Comput. 2007, 190:1795-1802.
    • (2007) Appl. Math. Comput. , vol.190 , pp. 1795-1802
    • Wang, Q.1
  • 30
    • 33751251025 scopus 로고    scopus 로고
    • Application of homotopy perturbation method in nonlinear heat conduction and convection equations
    • Ganji D.D., Sadighi A. Application of homotopy perturbation method in nonlinear heat conduction and convection equations. Phys. Lett. A 2007, 360:570-573.
    • (2007) Phys. Lett. A , vol.360 , pp. 570-573
    • Ganji, D.D.1    Sadighi, A.2
  • 31
    • 34250636701 scopus 로고    scopus 로고
    • The Application of He Homotopy perturbation and variational iteration method to nonlinear heat transfer and porous media equations
    • Ganji D.D. The Application of He Homotopy perturbation and variational iteration method to nonlinear heat transfer and porous media equations. J. Comput. Appl. Math. 2007, 207:24-34.
    • (2007) J. Comput. Appl. Math. , vol.207 , pp. 24-34
    • Ganji, D.D.1
  • 32
    • 61449224678 scopus 로고    scopus 로고
    • Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by an analytical technique
    • Ganji Z.Z., Ganji D.D., Rostamiyan Y. solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by an analytical technique. Appl. Math. Model 2009, 33:3107-3113.
    • (2009) Appl. Math. Model , vol.33 , pp. 3107-3113
    • Ganji, Z.Z.1    Ganji, D.D.2    Rostamiyan, Y.3
  • 33
    • 72449153908 scopus 로고    scopus 로고
    • Analytical study of Navier-Stokes equation with fractional orders using he's homotopy perturbation and variational iteration methods
    • Khan N.A., Ara A., Ali S.A. Analytical study of Navier-Stokes equation with fractional orders using he's homotopy perturbation and variational iteration methods. Int. J. Nonlinear Sci. Numer. 2009, 10:1127-1134.
    • (2009) Int. J. Nonlinear Sci. Numer. , vol.10 , pp. 1127-1134
    • Khan, N.A.1    Ara, A.2    Ali, S.A.3
  • 34
    • 67249166170 scopus 로고    scopus 로고
    • An algorithm for solving the fractional nonlinear Schrodinger equation by means of the homotopy perturbation method
    • Yildirim A. An algorithm for solving the fractional nonlinear Schrodinger equation by means of the homotopy perturbation method. Int. J. Nonlinear Sci. Numer. 2009, 10:445-450.
    • (2009) Int. J. Nonlinear Sci. Numer. , vol.10 , pp. 445-450
    • Yildirim, A.1
  • 35
    • 77953205877 scopus 로고    scopus 로고
    • The homotopy perturbation method for multi-order time fractional differential equations
    • Golbabai A., Sayevand K. The homotopy perturbation method for multi-order time fractional differential equations. Nonlinear sci. Lett. A 2010, 1:147-154.
    • (2010) Nonlinear sci. Lett. A , vol.1 , pp. 147-154
    • Golbabai, A.1    Sayevand, K.2
  • 36
    • 34748841026 scopus 로고    scopus 로고
    • Analytical solutions to the moving boundary problems with time-space fractional derivatives in drug release devices
    • Li X.C., Xu M.Y., Wang S.W. Analytical solutions to the moving boundary problems with time-space fractional derivatives in drug release devices. J. Phys. A: Math. Theor. 2007, 40:12131-12141.
    • (2007) J. Phys. A: Math. Theor. , vol.40 , pp. 12131-12141
    • Li, X.C.1    Xu, M.Y.2    Wang, S.W.3
  • 37
    • 58849156443 scopus 로고    scopus 로고
    • Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition
    • Li X.C., Xu M.Y., Jiang X.Y. Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition. Appl. Math. comput. 2009, 208:434-439.
    • (2009) Appl. Math. comput. , vol.208 , pp. 434-439
    • Li, X.C.1    Xu, M.Y.2    Jiang, X.Y.3
  • 38
    • 77953478412 scopus 로고    scopus 로고
    • Fractional calculus of variations in fractal spacetime
    • Wu G.C., He J.H. Fractional calculus of variations in fractal spacetime. Nonlinear Sci. Lett. A 2010, 1:281-287.
    • (2010) Nonlinear Sci. Lett. A , vol.1 , pp. 281-287
    • Wu, G.C.1    He, J.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.