Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order
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[1] O. Agrawal,et al. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .
[2] J. Cisternas,et al. Model of a two-dimensional extended chaotic system: evidence of diffusing dissipative solitons. , 2012, Physical review letters.
[3] S. Cox,et al. Exponential Time Differencing for Stiff Systems , 2002 .
[4] S. Bhardwaj,et al. Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients , 2016 .
[5] Mayya Tokman,et al. New Adaptive Exponential Propagation Iterative Methods of Runge-Kutta Type , 2012, SIAM J. Sci. Comput..
[6] V. Gafiychuk,et al. Mathematical modeling of time fractional reaction-diffusion systems , 2008 .
[7] Awad H. Al-Mohy,et al. Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators , 2011, SIAM J. Sci. Comput..
[8] I. Aranson,et al. The world of the complex Ginzburg-Landau equation , 2001, cond-mat/0106115.
[9] Fawang Liu,et al. A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker-Planck Equation , 2015, SIAM J. Sci. Comput..
[10] Effect of spatial configuration of an extended nonlinear Kierstead–Slobodkin reaction-transport model with adaptive numerical scheme , 2016, SpringerPlus.
[11] X. Li,et al. Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation , 2010 .
[12] Mihály Kovács,et al. Numerical solutions for fractional reaction-diffusion equations , 2008, Comput. Math. Appl..
[13] K. Patidar,et al. Numerical simulations of multicomponent ecological models with adaptive methods , 2016, Theoretical Biology and Medical Modelling.
[14] G. Wei,et al. High-order fractional partial differential equation transform for molecular surface construction , 2012 .
[16] Yangquan Chen,et al. Matrix approach to discrete fractional calculus II: Partial fractional differential equations , 2008, J. Comput. Phys..
[17] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .
[18] M. Haque,et al. Ratio-Dependent Predator-Prey Models of Interacting Populations , 2009, Bulletin of mathematical biology.
[19] Yong Zhou. Basic Theory of Fractional Differential Equations , 2014 .
[20] Emmanuel Hanert,et al. A comparison of three Eulerian numerical methods for fractional-order transport models , 2010 .
[21] P. Zhuang,et al. A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation , 2015, Appl. Math. Comput..
[22] Juan J. Trujillo,et al. Fractional Fourier transform in the framework of fractional calculus operators , 2010 .
[23] Fawang Liu,et al. Solving linear and non‐linear space–time fractional reaction–diffusion equations by the Adomian decomposition method , 2008 .
[24] R. Sahadevan,et al. Invariant analysis of nonlinear fractional ordinary differential equations with Riemann–Liouville fractional derivative , 2015 .
[25] Shaher Momani,et al. Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation , 2007 .
[26] Hongguang Sun,et al. Fractional diffusion equations by the Kansa method , 2010, Comput. Math. Appl..
[27] M. Garg,et al. NUMERICAL SOLUTION OF FRACTIONAL DIFFUSION-WAVE EQUATION WITH TWO SPACE VARIABLES BY MATRIX METHOD , 2010 .
[28] Fawang Liu,et al. Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy , 2015, SIAM J. Sci. Comput..
[29] Dumitru Baleanu,et al. Lagrangian Formulation of Classical Fields within Riemann-Liouville Fractional Derivatives , 2005 .
[30] M. Caputo. Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .
[31] Fawang Liu,et al. A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation , 2014, SIAM J. Numer. Anal..
[32] Mayya Tokman,et al. A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK) , 2011, J. Comput. Phys..
[33] S. Momani,et al. Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order , 2006 .
[34] S. Mancas,et al. Two-dimensional structures in the quintic Ginzburg–Landau equation , 2012, 1301.2997.
[35] R. Gorenflo,et al. AN OPERATIONAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES , 1999 .
[36] Kolade M. Owolabi,et al. Robust IMEX Schemes for Solving Two-Dimensional Reaction–Diffusion Models , 2015 .
[37] Xianjuan Li,et al. A Space-Time Spectral Method for the Time Fractional Diffusion Equation , 2009, SIAM J. Numer. Anal..
[38] I. Podlubny. Fractional differential equations , 1998 .
[39] Can Li,et al. A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative , 2011, 1109.2345.
[40] S. Momani,et al. A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula , 2008 .
[41] K. Miller,et al. An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .
[42] K. Burrage,et al. Fourier spectral methods for fractional-in-space reaction-diffusion equations , 2014 .
[43] Marlis Hochbruck,et al. Residual, Restarting, and Richardson Iteration for the Matrix Exponential , 2010, SIAM J. Sci. Comput..
[44] Qiang Du,et al. Analysis and Applications of the Exponential Time Differencing Schemes and Their Contour Integration Modifications , 2005 .
[45] Syed Tauseef Mohyud-Din,et al. Analytical Approach to Space- and Time-Fractional Burgers Equations , 2010 .
[46] M. Noor,et al. Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials , 2008 .
[47] S. Momani,et al. Numerical methods for nonlinear partial differential equations of fractional order , 2008 .
[48] K. Patidar,et al. Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations , 2015 .
[49] Hagberg,et al. From labyrinthine patterns to spiral turbulence. , 1994, Physical review letters.
[50] Yuri S Kivshar,et al. Ring dark solitons and vortex necklaces in Bose-Einstein condensates. , 2003, Physical review letters.
[51] Vu Thai Luan,et al. Explicit exponential Runge-Kutta methods of high order for parabolic problems , 2013, J. Comput. Appl. Math..
[52] Ahmed Alawneh,et al. Variational iteration method for solving the space‐ and time‐fractional KdV equation , 2008 .
[53] Stephen R. Baillie,et al. Modeling large-scale dispersal distances , 2002 .
[54] Fawang Liu,et al. Stability and convergence of an implicit numerical method for the space and time fractional Bloch–Torrey equation , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[55] Lloyd N. Trefethen,et al. Fourth-Order Time-Stepping for Stiff PDEs , 2005, SIAM J. Sci. Comput..
[56] S L Wearne,et al. Turing pattern formation in fractional activator-inhibitor systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.
[57] V. V. Gafiychuk,et al. Pattern formation in a fractional reaction diffusion system , 2006 .
[58] Kailash C. Patidar,et al. Higher-order time-stepping methods for time-dependent reaction-diffusion equations arising in biology , 2014, Appl. Math. Comput..
[59] H. Srivastava,et al. Theory and Applications of Fractional Differential Equations , 2006 .
[60] Hong Wang,et al. A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations , 2013, J. Comput. Phys..
[61] S. Ray,et al. Analytical solution for the space fractional diffusion equation by two-step Adomian Decomposition Method , 2009 .
[62] C. Lubich. Discretized fractional calculus , 1986 .
[63] Zaid M. Odibat,et al. Generalized Taylor's formula , 2007, Appl. Math. Comput..
[64] I. H. Abdel-Halim Hassan,et al. Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems , 2008 .
[65] Stefan Samko,et al. Denseness of the spaces $Φ_V$ of Lizorkin type in the mixed $L^{p̅}(ℝ^n)$-spaces , 1995 .
[66] A. Siddiqui,et al. Couette and Poiseuille Flows for Non-Newtonian Fluids , 2006 .
[67] M. Khader. On the numerical solutions for the fractional diffusion equation , 2011 .