Toward a new analytical method for solving nonlinear fractional differential equations
Tài liệu tham khảo
Beyer, 1995, Definition of physically consistent damping laws with fractional derivatives, Z. Angew. Math. Mech., 75, 623, 10.1002/zamm.19950750820
Caputo, 1967, Linear models of dissipation whose Q is almost frequency independent: Part II, J. Royal Astron. Soc., 13, 529, 10.1111/j.1365-246X.1967.tb02303.x
Diethelm, 2002, Analysis of fractional differential equations, J. Math. Anal. Appl., 265, 229, 10.1006/jmaa.2000.7194
Huang, 2005, The time-fractional diffusion equation and fractional advection–dispersion equation, ANZIAM J., 46, 1, 10.1017/S1446181100008282
Mainardi, 1996, Fractional relaxation–oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fract., 7, 1461, 10.1016/0960-0779(95)00125-5
Miller, 1993
Oldham, 1974
Podlubny, 1999
Torvik, 1996, On the appearance of the fractional derivative in the behavior of real materials, J. Appl. Mech., 51, 294, 10.1115/1.3167615
L. Blank, Numerical treatment of differential equations of fractional order, Numerical Analysis Report 287, Manchester Center for Computational.
Diethelm, 2005, Algorithms for the fractional calculus: a selection of numerical methods, Comput. Methods Appl. Mech. Engrg., 194, 743, 10.1016/j.cma.2004.06.006
Diethelm, 1997, Numerical solution for fractional differential equations by extrapolation, Numer. Algorithms, 16, 231, 10.1023/A:1019147432240
R. Gorenflo, Fractional calculus: some numerical methods, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus, New York, 1997.
Podlubny, 1997, Numerical solution of ordinary fractional differential equations by the fractional difference method
Daftardar-Gejji, 2006, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl., 316, 753, 10.1016/j.jmaa.2005.05.009
He, 1997, A new approach to nonlinear partial differential equations, Commun. Nonlinear Sci. Numer. Simul., 2, 230, 10.1016/S1007-5704(97)90007-1
He, 1998, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engrg., 167, 57, 10.1016/S0045-7825(98)00108-X
Adomian, 1994
Adomian, 1988, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135, 501, 10.1016/0022-247X(88)90170-9
Momani, 2006, Analytical solution of a time-fractional Navier–Stokes equation by Adomian decomposition method, Appl. Math. Comput., 177, 488, 10.1016/j.amc.2005.11.025
Odibat, 2006, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul., 7, 27, 10.1515/IJNSNS.2006.7.1.27
Odibat, 2007, Numerical solution of Fokker–Planck equation with space- and time-fractional derivatives, Phys. Lett. A, 369, 349, 10.1016/j.physleta.2007.05.002
Momani, 2007, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Solitons Fract., 31, 1248, 10.1016/j.chaos.2005.10.068
Momani, 2006, Analytical approach to linear fractional partial differential equations arising in fluid mechanics, Phys. Lett. A, 355, 271, 10.1016/j.physleta.2006.02.048
Inokuti, 1978, General use of the Lagrange multiplier in nonlinear mathematical physics, 156
He, 1997, Semi-inverse method of establishing generalized principles for fluid mechanics with emphasis on turbomachinery aerodynamics, Int. J. Turbo Jet-Engines, 14, 23, 10.1515/TJJ.1997.14.1.23
Finlayson, 1972
Reed, 1980