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Volumn 64, Issue 10, 2012, Pages 3075-3089

A numerical approach to the generalized nonlinear fractional Fokker-Planck equation

Author keywords

Fractional finite element method; L vy flight; Nonlinear fractional Fokker Planck equation; Riemann Liouville derivative

Indexed keywords

ERROR ESTIMATES; EXISTENCE AND UNIQUENESS; FRACTIONAL FOKKER-PLANCK EQUATION; FULLY DISCRETE; FULLY DISCRETE SCHEME; GALERKIN FINITE ELEMENT METHODS; NUMERICAL APPROACHES; NUMERICAL EXAMPLE; SPATIAL DIRECTION;

EID: 84868191489     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2012.01.067     Document Type: Article
Times cited : (23)

References (36)
  • 1
    • 0034238730 scopus 로고    scopus 로고
    • Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation
    • M. Bologna, C. Tsallis, and P. Grigolini Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation Phys. Rev. E 62 2000 2213 2218
    • (2000) Phys. Rev. e , vol.62 , pp. 2213-2218
    • Bologna, M.1    Tsallis, C.2    Grigolini, P.3
  • 2
    • 34548492507 scopus 로고    scopus 로고
    • Exact solution for nonlinear fractional anomalous diffusion equations
    • J.R. Liang, F.Y. Ren, W.Y. Qiu, and J.B. Xiao Exact solution for nonlinear fractional anomalous diffusion equations J. Phys. A 385 2007 80 94
    • (2007) J. Phys. A , vol.385 , pp. 80-94
    • Liang, J.R.1    Ren, F.Y.2    Qiu, W.Y.3    Xiao, J.B.4
  • 3
    • 0040307478 scopus 로고
    • Anomalous diffusion in disordered media: Statical mechanisms, models and physical applications
    • J. Bouchaud, and A. Georges Anomalous diffusion in disordered media: statical mechanisms, models and physical applications Phys. Rep. 195 1990 127 293
    • (1990) Phys. Rep. , vol.195 , pp. 127-293
    • Bouchaud, J.1    Georges, A.2
  • 4
    • 0001691616 scopus 로고
    • Observations of anomalous diffusion and Lévy flights in a 2-dimensional rotating flow
    • T.H. Solomon, E.R. Weeks, and H.L. Swinney Observations of anomalous diffusion and Lévy flights in a 2-dimensional rotating flow Phys. Rev. Lett. 71 1993 3975 3978
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 3975-3978
    • Solomon, T.H.1    Weeks, E.R.2    Swinney, H.L.3
  • 5
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, and J. Klafter The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 2000 1 77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 6
    • 0034113992 scopus 로고    scopus 로고
    • The fractional-order governing equation of Levy motion
    • DOI 10.1029/2000WR900032
    • D.A. Benson, S.W. Wheatcraft, and M.M. Meerschaeert The fractional order governing equations of Lévy motion Water Resour. Res. 36 2000 1413 1423 (Pubitemid 30334242)
    • (2000) Water Resources Research , vol.36 , Issue.6 , pp. 1413-1423
    • Benson, D.A.1    Wheatcraft, S.W.2    Meerschaert, M.M.3
  • 8
    • 0000885234 scopus 로고
    • Lévy dynamics of enhanced diffusion: Application to turbulence
    • M.F. Shlesinger, B.J. West, and J. Klafter Lévy dynamics of enhanced diffusion: application to turbulence Phys. Rev. Lett. 58 1987 1100 1103
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 1100-1103
    • Shlesinger, M.F.1    West, B.J.2    Klafter, J.3
  • 12
    • 85087253116 scopus 로고
    • Fractal distributions of reservoir heterogeneity and their influence on fluid transport
    • New Orleans, Louisiana
    • T.A. Hewett, Fractal distributions of reservoir heterogeneity and their influence on fluid transport, SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 1986.
    • (1986) SPE Annual Technical Conference and Exhibition
    • Hewett, T.A.1
  • 14
    • 0037365591 scopus 로고    scopus 로고
    • Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions
    • E.K. Lenzi, R.S. Mendes, L.C. Malacarne, and I.T. Pedron Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions Physica A 319 2003 245 252
    • (2003) Physica A , vol.319 , pp. 245-252
    • Lenzi, E.K.1    Mendes, R.S.2    Malacarne, L.C.3    Pedron, I.T.4
  • 15
    • 42749102157 scopus 로고    scopus 로고
    • Exact solutions to nonlinear nonautonomous space-fractional diffusion equations with absorption
    • E.K. Lenzi, G.A. Mendes, R.S. Mendes, L.R. da Silva, and L.S. Lucena Exact solutions to nonlinear nonautonomous space-fractional diffusion equations with absorption Phys. Rev. E 67 2003 051109
    • (2003) Phys. Rev. e , vol.67 , pp. 051109
    • Lenzi, E.K.1    Mendes, G.A.2    Mendes, R.S.3    Da Silva, L.R.4    Lucena, L.S.5
  • 16
    • 0036828775 scopus 로고    scopus 로고
    • Anomalous diffusion: Nonlinear fractional Fokker-Planck equation
    • C. Tsallis, and E.K. Lenzi Anomalous diffusion: nonlinear fractional Fokker-Planck equation Chem. Phys. 284 2002 341 347
    • (2002) Chem. Phys. , vol.284 , pp. 341-347
    • Tsallis, C.1    Lenzi, E.K.2
  • 17
    • 42649109055 scopus 로고    scopus 로고
    • Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation
    • DOI 10.1137/050642757
    • V.J. Ervin, H. Norbert, and J.P. Roop Numerical approximation of a time dependent nonlinear, space-fractional diffusion equation SIAM J. Numer. Anal. 45 2007 572 591 (Pubitemid 351599168)
    • (2007) SIAM Journal on Numerical Analysis , vol.45 , Issue.2 , pp. 572-591
    • Ervin, V.J.1    Heuer, N.2    Roop, J.P.3
  • 18
    • 33646262074 scopus 로고    scopus 로고
    • Variational formulation for the stationary fractional advection dispersion equation
    • V.J. Ervin, and J.P. Roop Variational formulation for the stationary fractional advection dispersion equation Numer. Methods Partial Differential Equations 22 2006 558 576
    • (2006) Numer. Methods Partial Differential Equations , vol.22 , pp. 558-576
    • Ervin, V.J.1    Roop, J.P.2
  • 19
    • 14644446063 scopus 로고    scopus 로고
    • Least squares finite-element solution of a fractional order two-point boundary value problem
    • DOI 10.1016/j.camwa.2004.10.003, PII S0898122104003438
    • G.J. Fix, and J.P. Roop Least squares finite-element solution of a fractional order two-point boundary value problem Comput. Math. Appl. 48 2004 1017 1033 (Pubitemid 40319749)
    • (2004) Computers and Mathematics with Applications , vol.48 , Issue.7-8 , pp. 1017-1033
    • Fix, G.J.1    Roof, J.P.2
  • 20
    • 61449085393 scopus 로고    scopus 로고
    • Computational algorithms for computing the fractional derivatives of functions
    • Z. Odibat Computational algorithms for computing the fractional derivatives of functions Math. Comput. Simulation 79 2009 2013 2020
    • (2009) Math. Comput. Simulation , vol.79 , pp. 2013-2020
    • Odibat, Z.1
  • 21
    • 69249214155 scopus 로고    scopus 로고
    • Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
    • Q. Yang, F. Liu, and I. Turner Numerical methods for fractional partial differential equations with Riesz space fractional derivatives Appl. Math. Model. 34 2010 200 218
    • (2010) Appl. Math. Model. , vol.34 , pp. 200-218
    • Yang, Q.1    Liu, F.2    Turner, I.3
  • 22
    • 76449122108 scopus 로고    scopus 로고
    • A note on the finite element method for the space-fractional advection diffusion equation
    • Y.Y. Zheng, C.P. Li, and Z.G. Zhao A note on the finite element method for the space-fractional advection diffusion equation Comput. Math. Appl. 59 2001 1718 1726
    • (2001) Comput. Math. Appl. , vol.59 , pp. 1718-1726
    • Zheng, Y.Y.1    Li, C.P.2    Zhao, Z.G.3
  • 23
    • 79251585926 scopus 로고    scopus 로고
    • A full discrete discontinuous Galerkin method for nonlinear fractional Fokker-Planck equation
    • Article ID: 279038
    • Y.Y. Zheng, C.P. Li, and Z.G. Zhao A full discrete discontinuous Galerkin method for nonlinear fractional Fokker-Planck equation Math. Probl. Eng. 2010 2010 Article ID: 279038
    • (2010) Math. Probl. Eng. , vol.2010
    • Zheng, Y.Y.1    Li, C.P.2    Zhao, Z.G.3
  • 24
    • 84855247929 scopus 로고    scopus 로고
    • A fully discrete Galerkin method for a nonlinear space-fractional diffusion equation
    • Article ID: 171620
    • Y.Y. Zheng, and Z.G. Zhao A fully discrete Galerkin method for a nonlinear space-fractional diffusion equation Math. Probl. Eng. 2011 2011 Article ID: 171620
    • (2011) Math. Probl. Eng. , vol.2011
    • Zheng, Y.Y.1    Zhao, Z.G.2
  • 25
    • 79960990048 scopus 로고    scopus 로고
    • Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
    • C.P. Li, Z.G. Zhao, and Y.Q. Chen Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion Commun. Math. Anal. 62 2011 855 875
    • (2011) Commun. Math. Anal. , vol.62 , pp. 855-875
    • Li, C.P.1    Zhao, Z.G.2    Chen, Y.Q.3
  • 28
    • 79953697124 scopus 로고    scopus 로고
    • Introduction to fractional integrability and differentiability
    • C.P. Li, and Z.G. Zhao Introduction to fractional integrability and differentiability Euro. Phys. J. - Special Topics 193 2011 5 26
    • (2011) Euro. Phys. J. - Special Topics , vol.193 , pp. 5-26
    • Li, C.P.1    Zhao, Z.G.2
  • 30
    • 34247212711 scopus 로고    scopus 로고
    • Remarks on fractional derivatives
    • C.P. Li, and W.H. Deng Remarks on fractional derivatives Appl. Math. Comput. 187 2007 777 784
    • (2007) Appl. Math. Comput. , vol.187 , pp. 777-784
    • Li, C.P.1    Deng, W.H.2
  • 31
    • 67349121725 scopus 로고    scopus 로고
    • Fractional derivatives in complex plane
    • C.P. Li, X.H. Dao, and P. Guo Fractional derivatives in complex plane Nonlinear Anal. TMA 71 2009 1857 1869
    • (2009) Nonlinear Anal. TMA , vol.71 , pp. 1857-1869
    • Li, C.P.1    Dao, X.H.2    Guo, P.3
  • 32
    • 79959248552 scopus 로고    scopus 로고
    • On Riemann-Liouville and Caputo derivatives
    • Article ID: 562494
    • C.P. Li, D.L. Qian, and Y.Q. Chen On Riemann-Liouville and Caputo derivatives Discrete Dyn. Nat. Soc. 2011 2011 Article ID: 562494
    • (2011) Discrete Dyn. Nat. Soc. , vol.2011
    • Li, C.P.1    Qian, D.L.2    Chen, Y.Q.3
  • 33
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    • N. Heymans, and I. Podlubny Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives Rheol. Acta 45 2006 765 772
    • (2006) Rheol. Acta , vol.45 , pp. 765-772
    • Heymans, N.1    Podlubny, I.2
  • 35
    • 0025416424 scopus 로고
    • Finite-element approximation of the nonstationary navier-stokes problem part IV. Error analysis for second-order time discretization
    • J.G. Heywood, and R. Rannacher Finite element approximation of the nonstationary Navier-Stokes problem, part IV: error analysis for the second-order time discretization SIAM J. Numer. Anal. 27 1990 353 384 (Pubitemid 20661046)
    • (1990) SIAM Journal on Numerical Analysis , vol.27 , Issue.2 , pp. 353-384
    • Heywood John, G.1    Rannacher Rolf2
  • 36
    • 49449119375 scopus 로고    scopus 로고
    • Numerical solution of the Fokker-Planck equation via Chebyschev polynomiations with reference to first passage time probability density functions
    • J. Reif, and R. Barakat Numerical solution of the Fokker-Planck equation via Chebyschev polynomiations with reference to first passage time probability density functions J. Comput. Phys. 23 1997 425 445
    • (1997) J. Comput. Phys. , vol.23 , pp. 425-445
    • Reif, J.1    Barakat, R.2


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