Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method
Tài liệu tham khảo
Adomian, 1988, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135, 501, 10.1016/0022-247X(88)90170-9
Adomian, 1994
K. Al-Khaled, D. Kaya, M.A. Noor, Numerical comparison of methods for solving parabolic equations, Appl. Math. Comput., in press
Agrawal, 2002, Solution for a fractional diffusion-wave equation defined in a bounded domain, Nonlinear Dynam., 29, 145, 10.1023/A:1016539022492
Andrezei, 2002, Multi-dimensional solutions of space-time-fractional diffusion equations, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci., 458, 429, 10.1098/rspa.2001.0893
Caputo, 1967, Linear models of dissipation whose Q is almost frequency independent. Part II, J. Roy. Astral. Soc., 13, 529, 10.1111/j.1365-246X.1967.tb02303.x
Cherrualt, 1989, Convergence of Adomian’s method, Kybernetes, 18, 31, 10.1108/eb005812
Cherrualt, 1993, Decomposition methods: a new proof of convergence, Math. Comput. Model., 18, 103, 10.1016/0895-7177(93)90233-O
M. Dehghan, Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specification, Appl. Math. Comput., in press
Fujita, 1990, Cauchy problems of fractional order and stable processes, Japan J. Appl. Math., 7, 459, 10.1007/BF03167854
Hilfer, 1995, Foundations of fractional dynamics, Fractals, 3, 549, 10.1142/S0218348X95000485
Hilfer, 2000, Fractional diffusion based on Riemann–Liouville fractional derivative, J. Phys. Chem., 104, 3914, 10.1021/jp9936289
Klafter, 1984, Fractal behavior in trapping and reaction: a random walk study, J. Stat. Phys., 36, 561, 10.1007/BF01012922
A.Y. Luchko, R. Groreflo, The initial value problem for some fractional differential equations with the Caputo derivative, Preprint series A08––98, fachbreich mathematik und informatik, Freic Universitat Berlin, 1998
Mainardi, 1997, Fractional calculus: Some basic problems in continuum and statistical mechanics, 291
Metzler, 2000, Boundary value problems fractional diffusion equations, Physica A, 278, 107, 10.1016/S0378-4371(99)00503-8
Miller, 1993
Oldham, 1974
Podlubny, 1999
Shawagfeh, 2001, Analytical approximate solutions for nonlinear fractional differential equations, Appl. Math. Comput., 123, 133
Wazwaz, 2002, Blow-up for solutions of some linear wave equations with mixed nonlinear boundary conditions, Appl. Math. Comput., 131, 517
Wazwaz, 2004, Exacat solution for heat-like and wave-like equations with variable coefficient, Appl. Math. Comput., 149, 51, 10.1016/S0096-3003(02)00946-3