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Volumn 16, Issue 11, 2011, Pages 4163-4173

The Legendre wavelet method for solving fractional differential equations

Author keywords

Fractional differential equations; Legendre wavelets; Operational matrices

Indexed keywords

DIFFERENTIAL EQUATIONS;

EID: 79957889333     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.01.014     Document Type: Article
Times cited : (209)

References (33)
  • 2
    • 10844270442 scopus 로고    scopus 로고
    • Application of fractional calculus to fluid mechanics
    • Kulish V.V., Lage José L. Application of fractional calculus to fluid mechanics. J Fluids Eng 2002, 124. 10.1115/1.1478062.
    • (2002) J Fluids Eng , vol.124
    • Kulish, V.V.1    Lage José, L.2
  • 3
    • 70350567183 scopus 로고    scopus 로고
    • Fractional differential equations in electrochemistry
    • Oldham K.B. Fractional differential equations in electrochemistry. Adv Eng Soft 2010, 41:9-12.
    • (2010) Adv Eng Soft , vol.41 , pp. 9-12
    • Oldham, K.B.1
  • 5
    • 0036650479 scopus 로고    scopus 로고
    • A predictor corrector approach for the numerical solution of fractional differential equation
    • Diethelm K., Ford N.J., Freed A.D. A predictor corrector approach for the numerical solution of fractional differential equation. Nonlin Dyn 2002, 29:3-22.
    • (2002) Nonlin Dyn , vol.29 , pp. 3-22
    • Diethelm, K.1    Ford, N.J.2    Freed, A.D.3
  • 7
    • 67649224114 scopus 로고    scopus 로고
    • Solving fractional integral equations by the Haar wavelet method
    • Lepik Ü. Solving fractional integral equations by the Haar wavelet method. Appl Math Comp 2009, 214:468-478.
    • (2009) Appl Math Comp , vol.214 , pp. 468-478
    • Lepik, Ü.1
  • 8
    • 0030649749 scopus 로고    scopus 로고
    • Haar wavelet method for solving lumped and distributed-parameter systems
    • Chen C., Hsiao C. Haar wavelet method for solving lumped and distributed-parameter systems. IEE P-Contr Theor Ap 1997, 144:8794.
    • (1997) IEE P-Contr Theor Ap , vol.144 , pp. 8794
    • Chen, C.1    Hsiao, C.2
  • 9
    • 34247336205 scopus 로고    scopus 로고
    • Kronecker operational matrices for fractional calculus and some applications
    • Kilicman A., Al Zhour Z.A.A. Kronecker operational matrices for fractional calculus and some applications. Appl Math Comp 2007, 187:250-265.
    • (2007) Appl Math Comp , vol.187 , pp. 250-265
    • Kilicman, A.1    Al Zhour, Z.A.A.2
  • 10
    • 74249095517 scopus 로고    scopus 로고
    • A new operational matrix for solving fractional-order differential equations
    • Saadatmandi A., Dehghan M. A new operational matrix for solving fractional-order differential equations. Comp Math Appl 2010, 59:1326-1336.
    • (2010) Comp Math Appl , vol.59 , pp. 1326-1336
    • Saadatmandi, A.1    Dehghan, M.2
  • 11
    • 77953135236 scopus 로고    scopus 로고
    • Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations
    • Li Yuanlu, Zhao Weiwei Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations. Appl Math Comput 2010, 216:2276-2285.
    • (2010) Appl Math Comput , vol.216 , pp. 2276-2285
    • Li, Y.1    Zhao, W.2
  • 12
    • 77949492283 scopus 로고    scopus 로고
    • Solving a nonlinear fractional differential equation using Chebyshev wavelets
    • Li Yuanlu Solving a nonlinear fractional differential equation using Chebyshev wavelets. Commun Nonl Sci Num Sim 2010, 15:2284-2292.
    • (2010) Commun Nonl Sci Num Sim , vol.15 , pp. 2284-2292
    • Li, Y.1
  • 13
    • 77957338653 scopus 로고    scopus 로고
    • A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order
    • Saeedi H., Mohseni Moghadam M., Mollahasani N., Chuev G.N. A CAS wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order. Commun Nonl Sci Num Sim 2011, 16:1154-1163.
    • (2011) Commun Nonl Sci Num Sim , vol.16 , pp. 1154-1163
    • Saeedi, H.1    Mohseni Moghadam, M.2    Mollahasani, N.3    Chuev, G.N.4
  • 14
    • 77957363391 scopus 로고    scopus 로고
    • Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets
    • Saeedi H., Mohseni Moghadam M. Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets. Appl Math Comput 2011, 16:1216-1226.
    • (2011) Appl Math Comput , vol.16 , pp. 1216-1226
    • Saeedi, H.1    Mohseni Moghadam, M.2
  • 15
    • 79957904209 scopus 로고    scopus 로고
    • Legendre wavelet method for numerical solutions of partial differential equations
    • Liu N., Lin En-Bing Legendre wavelet method for numerical solutions of partial differential equations. SIAM J Math Anal 1998, 29:1040-1065.
    • (1998) SIAM J Math Anal , vol.29 , pp. 1040-1065
    • Liu, N.1    Lin, E.-B.2
  • 16
    • 33750454785 scopus 로고    scopus 로고
    • Legendre wavelets method for solving differential equations of Lane-Emden type
    • Ali Yousefi S. Legendre wavelets method for solving differential equations of Lane-Emden type. Appl Math Comp 2006, 181:417-1422.
    • (2006) Appl Math Comp , vol.181 , pp. 417-1422
    • Ali Yousefi, S.1
  • 17
    • 75649107646 scopus 로고    scopus 로고
    • Techniques for solving integral and differential equations by Legendre wavelets
    • Zheng X., Yang X. Techniques for solving integral and differential equations by Legendre wavelets. Int J Syst Sci 2009, 40:1127-1137.
    • (2009) Int J Syst Sci , vol.40 , pp. 1127-1137
    • Zheng, X.1    Yang, X.2
  • 18
    • 33947199780 scopus 로고    scopus 로고
    • Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets
    • Maleknejad K., Sohrabi S. Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets. Appl Math Comput 2007, 186:836-843.
    • (2007) Appl Math Comput , vol.186 , pp. 836-843
    • Maleknejad, K.1    Sohrabi, S.2
  • 19
    • 0035323556 scopus 로고    scopus 로고
    • The Legendre wavelets operational matrix of integration
    • Razzaghi M., Yousefi S. The Legendre wavelets operational matrix of integration. Int J Syst Sci 2001, 32:495-502.
    • (2001) Int J Syst Sci , vol.32 , pp. 495-502
    • Razzaghi, M.1    Yousefi, S.2
  • 20
    • 31944442864 scopus 로고    scopus 로고
    • The linear Legendre mother wavelets operational matrix of integration and its application
    • Khellat F., Yousefi S.A. The linear Legendre mother wavelets operational matrix of integration and its application. J Frank Inst 2006, 343:181-190.
    • (2006) J Frank Inst , vol.343 , pp. 181-190
    • Khellat, F.1    Yousefi, S.A.2
  • 21
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent. Part II
    • Caputo M. Linear models of dissipation whose Q is almost frequency independent. Part II. J Roy Austral Soc 1967, 13:529-539.
    • (1967) J Roy Austral Soc , vol.13 , pp. 529-539
    • Caputo, M.1
  • 23
    • 25144460994 scopus 로고    scopus 로고
    • Positive solutions for boundary value problem of nonlinear fractional differential equation
    • Bai Z.B., Lü H.S. Positive solutions for boundary value problem of nonlinear fractional differential equation. J Math Anal Appl 2005, 311:495-505.
    • (2005) J Math Anal Appl , vol.311 , pp. 495-505
    • Bai, Z.B.1    Lü, H.S.2
  • 24
    • 55649098198 scopus 로고    scopus 로고
    • Boundary value problem for a coupled system of nonlinear fractional differential equations
    • Su X. Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl Math Lett 2009, 22:64-69.
    • (2009) Appl Math Lett , vol.22 , pp. 64-69
    • Su, X.1
  • 25
    • 0021439912 scopus 로고
    • On the appearance of the fractional derivative in the behavior of real materials
    • Bagley R.L., Torvik P.J. On the appearance of the fractional derivative in the behavior of real materials. ASME J Appl Mech 1984, 51:294-298.
    • (1984) ASME J Appl Mech , vol.51 , pp. 294-298
    • Bagley, R.L.1    Torvik, P.J.2
  • 26
    • 25644439033 scopus 로고    scopus 로고
    • Analytical solution of the Bagley-Torvik equation by Adomian decomposition method
    • Saha Ray S., Bera R.K. Analytical solution of the Bagley-Torvik equation by Adomian decomposition method. Appl Math Comp 2005, 168:398-410.
    • (2005) Appl Math Comp , vol.168 , pp. 398-410
    • Saha Ray, S.1    Bera, R.K.2
  • 27
    • 0012899160 scopus 로고    scopus 로고
    • Numerical solution of the Bagley-Torvik equation
    • Diethelm K., Ford N.J. Numerical solution of the Bagley-Torvik equation. Bit 2002, 42:490-507.
    • (2002) Bit , vol.42 , pp. 490-507
    • Diethelm, K.1    Ford, N.J.2
  • 28
    • 70449122559 scopus 로고    scopus 로고
    • General solution of the Bagley-Torvik equation with fractional-order derivative
    • Wang Z.H., Wang X. General solution of the Bagley-Torvik equation with fractional-order derivative. Commun Nonlin Sci Num Simul 2010, 15:1279-1285.
    • (2010) Commun Nonlin Sci Num Simul , vol.15 , pp. 1279-1285
    • Wang, Z.H.1    Wang, X.2
  • 29
    • 33745712076 scopus 로고    scopus 로고
    • An approximate method for numerical solution of fractional differential equations
    • Kumar P., Agrawal O.P. An approximate method for numerical solution of fractional differential equations. Signal Process 2006, 86:2602-2610.
    • (2006) Signal Process , vol.86 , pp. 2602-2610
    • Kumar, P.1    Agrawal, O.P.2
  • 30
    • 39149140685 scopus 로고    scopus 로고
    • Application of generalized differential transform method to multi-order fractional differential equations
    • Erturk V.S., Momani S., Odibat Z. Application of generalized differential transform method to multi-order fractional differential equations. Commun Nonlin Sci Num Simul 2008, 13:1642-1654.
    • (2008) Commun Nonlin Sci Num Simul , vol.13 , pp. 1642-1654
    • Erturk, V.S.1    Momani, S.2    Odibat, Z.3
  • 32
    • 33748425302 scopus 로고    scopus 로고
    • Numerical comparison of methods for solving linear differential equations of fractional order
    • Momani S., Odibat Z. Numerical comparison of methods for solving linear differential equations of fractional order. Chaos Solitons Fract 2007, 31:1248-1255.
    • (2007) Chaos Solitons Fract , vol.31 , pp. 1248-1255
    • Momani, S.1    Odibat, Z.2
  • 33
    • 34250215244 scopus 로고    scopus 로고
    • Solution of fractional differential equations by using differential transform method
    • Arikoglu A., Ozkol I. Solution of fractional differential equations by using differential transform method. Chaos Solitons Fract 2007, 34:1473-1481.
    • (2007) Chaos Solitons Fract , vol.34 , pp. 1473-1481
    • Arikoglu, A.1    Ozkol, I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.