Crank–Nicolson finite difference method for time-fractional coupled KdV equation

References

• M. Abbaszadeh, Error estimate of second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation, Appl. Math. Lett. 88 (2019), pp. 179–185.
   Web of Science ®Google Scholar
• M. Abbaszadeh, H. Amjadian, Second-order finite difference/spectral element formulation for solving the fractional advection-diffusion equation, Commun. Appl. Math. Computation 2(4) (2020), pp. 653–669.
   Google Scholar
• M. Abbaszadeh, M. Dehghan, and Y. Zhou, Crank-Nicolson/Galerkin spectral method for solving two dimensional time-space distributed-order weakly singular integro-partial differential equation, J. Comput. Appl. Math. 374 (2020), pp. 112739.
   Google Scholar
• B. Albuohimad, H. Adibi, S. Kazem, A numerical solution of time-fractional coupled Korteweg–de vries equation by using spectral collocation method, Ain Shams Eng. J. 9(4) (2018), pp. 1897–1905.
   Web of Science ®Google Scholar
• A.H. Bhrawy, E.H. Doha, S.S. Ezz-Eldien, and M.A. Abdelkawy, A numerical technique based on the shifted Legendre polynomials for solving the time fractional coupled KdV equations, Calcolo 53 (2015), pp. 1–17.
   Web of Science ®Google Scholar
• S.A. El-Wakil, E.M. Abulwafa, E.K. El-Shewy, and A.A. Mahmoud, Time-fractional KdV equation for plasma of two different temperature electrons and stationary ion, Phys. Plasmas 18 (2011), pp. 092116.
   Web of Science ®Google Scholar
• S.A. El-Wakil, E.M. Abulwafa, M.A. Zahran, and A.A. Mahmoud, Time-fractional KdV equation: formulation and solution using variational methods, Nonlinear Dyn. 65 (2011), pp. 55–63.
   Web of Science ®Google Scholar
• J.H. He, Approximate analytical solution for seepage flow with fractional derivative in porous media, Comput. Methods Appl. Mech. Eng. 167 (1998), pp. 69–73.
   Web of Science ®Google Scholar
• R. Herrmann, Folded potentials in cluster physics–a comparison of Yukawa and Coulomb potentials with Riesz fractional integrals, J. Phys. A 46(40) (2013), pp. 405203. 12 pp.
   Google Scholar
• R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific Publishing, River Edge, NJ, 2000.
   Google Scholar
• R. Hirota and J. Satsuma, Soliton solutions of a coupled Korteweg–de Vries equation, Phys. Lett. A85 (1981), pp. 407–408.
   Web of Science ®Google Scholar
• A. Korkmaz and O.E. Hepson, Hyperbolic tangent solution to the conformable time fractional Zakharov–Kuznetsov equation in 3D space, AIP Conf. Proc. 1926 (2018), pp. 020023.
   Google Scholar
• A. Korkmaz, O.E. Hepson, K. Hosseini, H. Rezazadeh, and M. Eslami, Sine–Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class, J. King Saud University -- Sci. 32(1) (2020), pp. 567–574.
   Web of Science ®Google Scholar
• C.P. Li and W.H. Deng, Remarks on fractional derivatives, Appl. Math. Comput. 187 (2007), pp. 777–784.
   Web of Science ®Google Scholar
• G Li and H Liu, Stability analysis and synchronization for a class of fractional-order neural networks, Entropy 18 (2016), pp. 55. 13 pp.
   Web of Science ®Google Scholar
• X.J. Li and C.J. Xu, A space-time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal. 47 (2009), pp. 2108–2131.
   Web of Science ®Google Scholar
• C.P. Li, Z.G. Zhao, Numerical approximation of nonlinear fractional differential equations with sub diffusion and super diffusion, Comput. Math. Appl. 62(3) (2011), pp. 855–875.
   Web of Science ®Google Scholar
• J.-C. Liu and G.-L. Hou, New approximate solution for time-fractional coupled KdV equations by generalized differential transform method, Chin. Phys. B 19(11) (2010), pp. 110203.
   Google Scholar
• F Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial college press, London, 2010.
   Google Scholar
• M.M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection dispersion, J. Comput. Appl. Math. 172 (2004), pp. 65–77.
   Web of Science ®Google Scholar
• M. Merdan and S.T. Mohyud-Din, A new method for time-fractional coupled KDV equations with modified Riemann–Liouville derivative, Stud. Nonlinear Sci. 2(2) (2011), pp. 77–86.
   Google Scholar
• T Odzijewicz, A.B. Malinowska, and D.F.M Torres, A generalized fractional calculus of variations, Control Cybern 42(2) (2013), pp. 443–458.
   Google Scholar
• K.B. Oldham and J Spanier, The Fractional Calculus, Academic Press, New York, 1974.
   Google Scholar
• E.C. Oliveira and J.A.T Machado, Review of definitions for fractional derivatives and integral, A Math. Probl. Eng. 2014 (2014), pp. 238–459. 6 pp.
   Web of Science ®Google Scholar
• L. Ostrovsky and Y.A. Stepanyants, Do internal solutions exist in the ocean?, Rev. Geophys. 27 (1989), pp. 293–310.
   Web of Science ®Google Scholar
• C Pinto and A.R.M Carvalho, New findings on the dynamics of HIV and TB coinfection models, Appl. Math. Comput. 242 (2014), pp. 36–46.
   Web of Science ®Google Scholar
• I Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, 1999.
   Google Scholar
• D Sierociuk, T Skovranek, M Macias, I Podlubny, I Petras, A Dzielinski, and P Ziubinski, Diffusion process modeling by using fractional-order models, Appl. Math. Comput. 257(15) (2015), pp. 2–11. 4 pp.
   Web of Science ®Google Scholar
• A Umair, A Farah Aini, and I. Ahmad Izani, Crank-Nicolson finite difference method for two-dimensional fractional sub-diffusion equation, J. Interpolation Approx. Sci. Computing 2 (2017), pp. 18–29.
   Google Scholar