A predictor-corrector scheme for solving the time fractional Fokker-Planck equation with uniform and non-uniform meshes
暂无分享,去创建一个
[1] Robert J. Marks,et al. Differintegral interpolation from a bandlimited signal's samples , 1981 .
[2] T. Goudon,et al. On a Fokker-Planck equation arising in population dynamics , 1998 .
[3] Weihua Deng,et al. Numerical algorithm for the time fractional Fokker-Planck equation , 2007, J. Comput. Phys..
[4] J. David Logan,et al. Transport Modeling in Hydrogeochemical Systems , 2001 .
[5] Yujiang Wu,et al. Efficient algorithms for solving the fractional ordinary differential equations , 2015, Appl. Math. Comput..
[6] W. Schneider,et al. Fractional diffusion and wave equations , 1989 .
[7] Mahdi Saedshoar Heris,et al. A predictor–corrector scheme for the tempered fractional differential equations with uniform and non-uniform meshes , 2019, The Journal of Supercomputing.
[8] K. B. Oldham,et al. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .
[9] D. C. Hong. Effect of Excluded Volume and Anisotropy on Granular Statistics , 1999, cond-mat/9909252.
[10] Mahdi Saedshoar Heris,et al. On FBDF5 Method for Delay Differential Equations of Fractional Order with Periodic and Anti-Periodic Conditions , 2017 .
[11] Alan D. Freed,et al. Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.
[12] R. F. Escobar-Jiménez,et al. Analytical and numerical solutions of electrical circuits described by fractional derivatives , 2016 .
[13] Xuenian Cao,et al. Numerical Method for The Time Fractional Fokker-Planck Equation , 2012 .
[14] Chaozhen Wei,et al. A Fokker–Planck reaction model for the epitaxial growth and shape transition of quantum dots , 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[15] P Hänggi,et al. Fractional Fokker-Planck dynamics: Numerical algorithm and simulations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.
[16] Da Xu,et al. A backward euler orthogonal spline collocation method for the time‐fractional Fokker–Planck equation , 2015 .
[17] Mario Di Paola,et al. Fractional characteristic times and dissipated energy in fractional linear viscoelasticity , 2016, Commun. Nonlinear Sci. Numer. Simul..
[18] H. Srivastava,et al. Theory and Applications of Fractional Differential Equations , 2006 .
[19] Mahdi Saedshoar Heris,et al. On fractional backward differential formulas for fractional delay differential equations with periodic and anti-periodic conditions , 2017 .
[20] Zhen Wang,et al. Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay , 2011, Comput. Math. Appl..
[21] R. Magin. Fractional Calculus in Bioengineering , 2006 .
[22] Philippe Marcq,et al. On the stochastic pendulum with Ornstein-Uhlenbeck noise , 2004, cond-mat/0407198.
[23] Mohammad Javidi,et al. A predictor-corrector scheme for solving nonlinear fractional differential equations with uniform and nonuniform meshes , 2019, Int. J. Model. Simul. Sci. Comput..
[24] A. D. Fokker. Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld , 1914 .
[25] Yingjun Jiang. A new analysis of stability and convergence for finite difference schemes solving the time fractional Fokker–Planck equation , 2015 .
[26] E. Barkai,et al. Fractional Fokker-Planck equation, solution, and application. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.
[27] H. Srivastava,et al. Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .
[28] Sachin Bhalekar,et al. A new predictor-corrector method for fractional differential equations , 2014, Appl. Math. Comput..
[29] R. Bagley,et al. Fractional order state equations for the control of viscoelasticallydamped structures , 1991 .
[30] Masatoshi Shiino,et al. Stability analysis of mean-field-type nonlinear Fokker-Planck equations associated with a generalized entropy and its application to the self-gravitating system. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[31] Fawang Liu,et al. Finite difference approximations for the fractional Fokker–Planck equation , 2009 .
[32] Fan Yang,et al. On the definition of fractional derivatives in rheology , 2011 .
[33] H. C. Ottinger,et al. Dynamic mean-field models from a nonequilibrium thermodynamics perspective. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[34] Tian Jian Lu,et al. Fractional order generalized electro-magneto-thermo-elasticity , 2013 .
[35] M. Dehghan,et al. The Sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients , 2012 .