[1] Al-Mdallal, Q. and Syam, M. An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order, Commun. Nonlinear Sci. Numer. Simul. 17(6) (2012) 2299–2308.
[2] Atangana, A. and Goufo, E. Extension of matched asymptotic method to fractional boundary layers problems, Math. Probl. Eng. (2014) 2014.
[3] Bijura, A.M. Nonlinear singular perturbation problems of arbitrary real orders, 2003.
[4] Caputo, M. and Fabrizio, M. A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl. 1(2) (2015) 73–85.
[5] Cooke, K. Differential—difference equations, In International symposium on nonlinear differential equations and nonlinear mechanics, pages 155–171. Elsevier, 1963.
[6] Diekmann, O., Gils, S., Lunel, S. and Walther, H. Delay equations: functional-, complex-, and nonlinear analysis, volume 110. Springer Science & Business Media, 2012.
[7] Driver, R. Ordinary and delay differential equations, volume 20. Springer Science & Business Media, 2012.
[8] Gelu, F. and Duressa, G. Hybrid method for singularly perturbed robin type parabolic convection–diffusion problems on shishkin mesh, Partial Differ. Equ. Appl. Math. 8:100586, 2023.
[9] Govindarao, L. and Mohapatra, J. A second order numerical method for singularly perturbed delay parabolic partial differential equation, Eng. Comput. 36(2) (2018) 420–444.
[10] Hailu, W. and Duressa, G. Accelerated parameter-uniform numerical method for singularly perturbed parabolic convection-diffusion problems with a large negative shift and integral boundary condition. Result. Appl. Math. 18 (2023) 100364.
[11] Hailu, W. and Duressa, G. Uniformly convergent numerical scheme for solving singularly perturbed parabolic convection-diffusion equations with integral boundary condition, Differ. Equ. Dyn. Syst. (2023) 1–27 .
[12] Hailu, W. and Duressa, G. A robust collocation method for singularly perturbed discontinuous coefficients parabolic differential difference equations, Research in Mathematics, 11(1) (2024) 2301827.
[13] Hale, J. and Lunel, S. Introduction to functional differential equations, volume 99. Springer Science & Business Media, 2013.
[14] Hassen, Z. and Duressa, G. Parameter uniform hybrid numerical method for time-dependent singularly perturbed parabolic differential equations with large delay, Appl. Math. Sci. Eng. 32(1) (2024) 2328254.
[15] Kolmanovskii, V. and Myshkis, A. Applied theory of functional differential equations, volume 85. Springer Science & Business Media, 2012.
[16] Kolmanovskii, V. and Nosov, V. Stability of functional differential equations, volume 180. Elsevier, 1986.
[17] Kuang, Y. Delay differential equations: with applications in population dynamics. Academic press, 1993.
[18] Kumar, K. and Vigo-Aguiar, J. Numerical solution of time-fractional singularly perturbed convection–diffusion problems with a delay in time, Math. Method. Appl. Sci. 44(4) (2021) 3080–3097.
[19] Losada, J. and Nieto, J. Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl. 1(2) (2015) 87–92.
[20] Meerschaert, M. and Tadjeran, C. Finite difference approximations for two-sided space-fractional partial differential equations, Applied numerical mathematics, 56(1) (2006) 80–90.
[21] Miller, J., O’riordan, E, and Shishkin, G. Fitted numerical methods for singular perturbation problems: error estimates in the maximum norm for linear problems in one and two dimensions. World scientific, 2012.
[22] Miller, P. Applied asymptotic analysis, volume 75. American Mathematical Soc., 2006.
[23] Negero, N. and Duressa, G. A method of line with improved accuracy for singularly perturbed parabolic convection–diffusion problems with large temporal lag, Results Appl. Math. 11 (2021) 100174.
[24] Negero, N. and Duressa, G. An exponentially fitted spline method for singularly perturbed parabolic convection-diffusion problems with large time delay, Tamkang J. Math., 54(4) (2023) 313–338.
[25] Nelson, P. and Perelson, A. Mathematical analysis of delay differential equation models of HIV-1 infection, Math.Biosci., 179(1) (2002) 73–94.
[26] Norkin, S. Introduction to the theory and application of differential equations with deviating arguments. Academic Press, 1973.
[27] Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. elsevier, 1998.
[28] Podlubny, I. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Math. Sci. Eng. 198 (340) (1999) 0924–34008.
[29] Rangaig, N. and Pido, A. Finite difference approximation method for two-dimensional space-time fractional diffusion equation using nonsingular fractional derivative. Prog. Fract. Differ. Appl, 5(4) (2019) 1–11.
[30] Roop, J. Numerical approximation of a one-dimensional space fractional advection–dispersion equation with boundary layer, Comput. Math. Appl. 56(7) (2008) 1808–1819.
[31] Roos, H., Stynes, M. and Tobiska, L. Robust numerical methods for singularly perturbed differential equations: convection-diffusion-reaction and flow problems, volume 24. Springer Science & Business Media, 2008.
[32] Sadri, K. and Aminikhah, H. An efficient numerical method for solving a class of variable-order fractional mobile-immobile advection-dispersion equations and its convergence analysis, Chaos, Solitons Fractals, 146 (2021) 110896.
[33] Sahoo, S. and Gupta, V. A robust uniformly convergent finite difference scheme for the time-fractional singularly perturbed convection-diffusion problem, Comput. Math. Appl. 137 (2023) 126–146.
[34] Sayevand, K. and Pichaghchi, K. Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order, Commun. Nonlinear Sci. Numer. Simul., 57 (2018) 136–168.
[35] Sayevand, K. and Pichaghchi, K. A novel operational matrix method for solving singularly perturbed boundary value problems of fractional multi-order, Int. J. Comput. Math. 95(4) (2018) 767–796.
[36] Shakti, D., Mohapatra, J., Das, P. and Vigo-Aguiar, J. A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction–diffusion problems with arbitrary small diffusion terms, J. Comput. Appl. Math. 404 (2022) 113167.
[37] Villasana, M. and Radunskaya, A. A delay differential equation model for tumor growth, J. Math. Bio. 47 (2003) 270–294.
[38] Yuste, S. and Acedo, L. An explicit finite difference method and a new von neumann-type stability analysis for fractional diffusion equations, SIAM J. Numer. Anal. 42(5) (2005) 1862–1874.
[39] Zhao, T. Global periodic-solutions for a differential delay system modeling a microbial population in the chemostat, J. Math. Anal. Appl. 193(1) (1995) 329–352.
