Analytical solution of the time fractional Navier-Stokes equation
Tài liệu tham khảo
Abu Arqoub, 2013, A reliable analytical method for solving higher-order initial value problems, Discr. Dynam. Nat. Soc., 10.1155/2013/673829
Abu Arqoub, 2013, Series solutions of fuzzy differential equations under strongly generalized differentiability, Jaram, 5, 31, 10.5373/jaram.1447.051912
Abu Arqoub, 2015, Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations, J. Comput. Phys., 293, 385, 10.1016/j.jcp.2014.09.034
Abu Arqoub, 2014, Multiple solutions of nonlinear boundary value problems of fractional order: a new analytic iterative technique, Entropy, 16, 471, 10.3390/e16010471
Abu Arqoub, 2013, A representation of the exact solution of generalized lane-Emden equations using a new analytic method, Abstr. Appl. Anal., 10.1155/2013/378593
Alquran, 2014, Analytical solutions of fractional foam drainage equation by residual power series method, Math. Sci., 8, 153, 10.1007/s40096-015-0141-1
Alquran, 2015, Analytical solutions of time fractional two-component evolutionary system of order 2 by residual power series method, J. Appl. Anal. Comput., 5, 589
Armfield, 2000, fractional step methods for the Navier-Stokes equations on non-staggered grids, ANZIAM J., 42, c134, 10.21914/anziamj.v42i0.593
Chaurasia, 2011, Solution of the time-fractional Navier-Stokes equation, Gen. Math. Notes, 4, 49
Chorin, 1968, Numerical solution of the Navier-Stokes equations, Math. Comp., 22, 754, 10.1090/S0025-5718-1968-0242392-2
Diethelm, 2004
El-Ajou, 2013, New results on fractional power series: theories and applications, Entropy, 15, 5305, 10.3390/e15125305
El-Ajou, 2015, A novel expansion iterative method for solving linear partial differential equations of fractional order, Appl. Math. Comput., 257, 119
El-Ajou, 2015, Approximate analytical solution of the nonlinear fractional Kdv-Burgers equation: a new iterative algorithm, J. Comput. Phys., 293, 81, 10.1016/j.jcp.2014.08.004
Kilbas, 2006
Kim, 1985, Application of a fractional step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59, 308, 10.1016/0021-9991(85)90148-2
Kumar, 2014, Analytical solution of fractional Navier-Stokes equation by using modified Laplace decomposition method, Ain Shams Eng. J., 5, 569, 10.1016/j.asej.2013.11.004
Liao, 2004, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput., 147, 499
Lin, 2013, Laplace transform for solving some families of fractional differential equations and its applications, Adv. Diff. Eq., Springer Open J., 137
Momani, 2006, Analytical solution of a time-fractional Navier-Stokes equation by adomian decomposition method, Appl. Math. Comput., 177, 488
Oldham, 1974
C.E. Pearson, Computational Method for Time Dependent Two Dimensional Incompressible Viscous Flow Problems, Sperry-Rand Research Center, Sudbury, Mass., Report No. SRRC-RR-64-17, 1964.
Perot, 1993, An analysis of the fractional step method, J. Comput. Phys., 108, 51, 10.1006/jcph.1993.1162
Podlubny, 1994
Samko, 1993
Singh, 2014, Numerical solutions of nonlinear fractional partial differential equations arising in spatial diffusion of biological populations, Abstr. Appl. Anal., 10.1155/2014/535793
choudhary, 2016, Numerical simulation of a fractional model of temperature distribution and heat flux in the semi-infinite solid, Alex. Eng. J., 55, 87, 10.1016/j.aej.2016.01.007
Sarwar, 2016, Approximate solution of two-term fractional-order diffusion, wave-diffusion, and the telegraph models arising in mathematical physics using optimal homotopy asymptotic method, Waves Rand. Comp. Media, 10.1080/17455030.2016.1158436
Yang, 2014, Application of local fractional series expansion method to solve Klein-Gordon equations on cantor sets, Abstr. Appl. Anal.
Kumar, 2015, A fractional model of Navier-Stokes equation arising in unsteady flow of a viscous fluid, J. Assoc. Arab Univ. Basic Appl. Sci., 17, 14
Kumar, 2016, Numerical computation of a fractional model of differential-difference equation, J. Comput. Nonlin. Dynam., 11, 10.1115/1.4033899
Kumar, 2014, Numerical computation of fractional Black-Scholes equation arising in financial market, Egypt. J. Basic Appl. Sci., 1, 177, 10.1016/j.ejbas.2014.10.003