[1] Benson A D, Wheatcraft W S, Meerschaert M M. The fractional-order governing equation of Lévy motion. Water Resour Res, 2000, 36(6):1413-1424 [2] Chang C M, Liu F, Burrage K. Numerical analysis for a variable-order nonlinear cable equation. J Comput Appl Math, 2011, 236(2):209-224 [3] Chen Chang-Ming, Liu F, Anh V, Turner I. Numerical schemes with high spatial accuracy for a variableorder anomalous subdiffusion equation. SIAM J Sci Comput, 2010, 32(4):1740-1760 [4] Henry I B, Langlands M A T, Wearne L S. Fractional cable models for spiny neuronal dendrites. Phys Rev Lett, 2008, 100:128103pp [5] Ingman D, Suzdalnitsky J. Control of damping oscillations by fractional differential operator with timedependent order. Comput Methods Appl Mech Eng, 2004, 193(52):5585-5595 [6] Ingman D, Suzdalnitsky J, Zeifman M. Constitutive dynamic-order model for nonlinear contact phenomena. J Appl Mech, 2000, 67(2):383-390 [7] Kilbas A A, Srivastava M H, Trujillo J J. Theory and applications of fractional differential equations. San Diego:Elsevier, 2006 [8] Langlands M A T, Henry I B, Wearne L S. Fractional cable equation models for anomalous electrodiffusion in nerve cells:infinite domain solutions. J Math Biol, 2009, 59(6):761-808 [9] Liu F, Zhuang P, Anh V, Turner I. A fractional-order implicit difference approximation for the space-time fractional diffusion equation. ANZIAM J, 2006, 47:C48-684 [10] Lorenzo C F, Hartley T T. Variable order and distributed order fractional operators. Nonlinear Dyn, 2002, 29:57-98 [11] Lorenzo C F, Hartley T T. Initialized fractional calculus. Internat J Appl Math, 2000, 3(3):249-265 [12] Lubich C. Discretized fractional calculus. SIAM J Math Anal, 1986, 17:704-719 [13] Nagy A M, Sweilam N H. An efficient method for solving fractional Hodgkin-Huxley model. Phys Lett A, 2014, 378:1980-1984 [14] Podlubny I. Fractional differential equations. San Diego:Academic Press, 1999 [15] Podlubny I, El-Sayed A M A. On two definitions of fractional derivatives. Slovak Academy of Sciences, Institute of Experimental Physics, 1996:ISBN 80-7099-252-2 [16] Quintana-Murillo J, Yuste B S. An explicit numerical method for the fractional cable equation. Int J Differential Equations, 2011, 2011:12pp [17] Ramirez L E S, Coimbra C F M. On the selection and Meaning of variable order operators for dynamic modeling. Int J Differ Equat, 2010, 2010:16pp [18] Ramirez L E S, Coimbra C F M. A variable order constitutive relation for viscoelasticity. Ann Phys, 2007, 16(7/8):543-552 [19] Reynolds A. On the anomalous diffusion characteristics of membrane bound proteins. Phys Lett A, 2005, 342:439-442 [20] Samko S G, Ross B. Integration and differentiation to a variable fractional order. Integral Transforms Spec Funct, 1993,1(4):277-300 [21] Sweilam N H, Khader M M, Nagy A M. Numerical solution of two-sided space-fractional wave equation using finite difference method. J Comput Appl Math, 2011, 235(8):2832-2841 [22] Sweilam N H, Nagy A M. Numerical solution of fractional wave equation using Crank-Nicolson method. World Appl Sci J, 2011, 13(Special Issue of Applied Math):71-75 [23] Sweilam N H, Nagy A M, El-Sayed Adel A. Second kind shifted Chebyshev polynomials for solving space fractional order diffusion equation. Chaos Solitons Fractals, 2015, 73:141-147 [24] Sweilam N H, Nagy A M, Assiri T A, Ali N Y. Numerical simulations for variable-order fractional nonlinear differential delay equations. J Fract Calc Appl, 2015, 6(1):71-82 [25] Sweilam N H, Assiri T A. Numerical simulations for the space-time variable order nonlinear fractional wave equation. J Appl Math, 2013, 2013:7pp |