References
- Hwang C, Cheng YC. A numerical algorithm for stability testing of fractional delay systems. Automatica. 2006;42:825–831.
- Davis LC. Modification of the optimal velocity traffic model to include delay due to driver reaction time. Physica A. 2002;319:557–567.
- Kuang Y. Delay differential equations with applications in population biology. Boston (MA): Academic Press; 1993.
- Bellen A, Zennaro M. Numerical methods for delay differential equations. Oxford: Oxford University Press; 2003.
- Podlubny I. Fractional differential equations. New York (NY): Academic Press; 1999.
- Chen Y, Moore KL. Analytical stability bound for a class of delayed fractional-order dynamic systems. Nonlinear Dyn. 2002;29:191–200.
- Zhang X. Some results of linear fractional order time-delay system. Appl. Math. Comput. 2008;197:407–411.
- Zhou Y, Jiao F, Li J. Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 2009;71:3249–3256.
- Ouyang Z. Existence and uniqueness of the solutions for a class of nonlinear fractional order partial differential equations with delay. Comput. Math. Appl. 2011;61:860–870.
- Yang Z, Cao J. Initial value problems for arbitrary order fractional differential equations with delay. Commun. Nonlinear Sci. Numer. Simul. 2013;18:2993–3005.
- Deng W, Wu Y, Li C. Stability analysis of differential equations with time-dependent delay. Int. J. Bifurcation Chaos. 2006;16:465–472.
- Deng W, Li C, Lü J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn. 2007;48:409–416.
- Samko S, Kilbas A, Marichev O. Fractional integrals and derivatives: theory and applications. Basel: Gordon and Breach; 1993.
- Shen S, Liu F, Anh V. Fundamental solution and discrete random walk model for a time-space fractional diffusion equation of distributed order. J. Appl. Math. Comput. 2008;28:147–164.
- Bhalekar S, Daftardar-Gejji V. A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order. J. Fract. Calcu. Appl. 2011;1:1–8.
- Daftardar-Gejji V, Sukale Y, Bhalekar S. Solving fractional delay differential equations: a new approach. Fract. Calc. Appl. Anal. 2015;18:400–418.
- Khader MM, Hendy AS. The approximate and exact solutions of the fractional-order delay differential equations using Legendre pseudospectral method. Int. J. Pure Appl. Math. 2012;74:287–297.
- Wang Z, Huang X, Zhou J. A numerical method for delayed fractional-order differential equations: Based on G-L definition. Appl. Math. Inf. Sci. 2013;7:525–529.
- Moghaddam B, Yaghoobi S, Machado J. An extended predictor-corrector algorithm for variable-order fractional delay differential equations. J. Comput. Nonlinear Dyn. 2016. doi:10.11.1115/1.4032574.
- Rihan FA. Computational methods for delay parabolic and time-fractional partial differential equations. Numer. Method Partial Differ. Equ. 2010;26:1556–1571.
- Sakara M, Uludag F, Erdogan F. Numerical solution of time-fractional nonlinear PDEs with proportional delays by homotopy perturbation method. Appl. Math. Model. 2016;000:1–11.
- Oldham KB, Spanier J. The Fractional Calculus. New York (NY): Academic Press; 1974.
- Zhang Q, Zhang C. A new linearized compact multisplitting scheme for the nonlinear convection-reaction-diffusion equations with delay. Commun. Nonlinear Sci. Numer. Simul. 2013;18:3278–3288.
- Marzban HR, Tabrizidooz HR. A hybrid approximation method for solving Hutchinson’s equation. Commun. Nonlinear Sci. Numer. Simul. 2012;17:100–119.
- Li D, Wen J. A note on compact finite difference method for reaction-diffusion equations with delay. Appl. Math. Model. 2015;39:1749–1754.
- Li D, Zhang C. L∞ error estimates of discontinuous Galerkin methods for delay differential equations. Appl. Numer. Math. 2014;82:1–10.
- Zhang Q, Zhang C. A compact difference scheme combined with extrapolation techniques for solving a class of neutral delay parabolic differential equations. Appl. Math. Lett. 2013;26:306–312.
- Liao W. A compact high-order finite difference method for unsteady convection-diffusion equation. Int. J. Comput. Methods Eng. Sci. Mech. 2012;13:135–145.
- Sun Z, Wu X. A fully discrete difference scheme for a diffusion-wave system. Appl. Numer. Math. 2006;56:193–209.
- Chen S, Liu F, Zhuang P, et al. Finite difference approximations for the fractional Fokker--Planck equation. Appl. Math. Model. 2009;33:256–273.
- Samarskii A, Andreev B. Finite difference methods for elliptic equation. Moscow: Nauka; 1976. Chinese; Beijing: Science Press; 1984. Chinese.
- Sun Z. The numerical methods for partial differential equations. Beijing: Science Press; 2005. Chinese.
- Holte JM. Discrete Gronwall lemma and applications. Grand Forks (ND): MAA-NCS meeting at the university of North Dakota. 2009.