Numerical Treatment of the Fractional Modeling on Susceptible-Infected-Recovered Equations with a Constant Vaccination Rate by Using GEM

References

[1] S. Das and P. K. Gupta, A mathematical model on fractional Lotka-Volterra equations, J. Theor. Bio. 277 (2011), 1–6.10.1016/j.jtbi.2011.01.034Search in Google Scholar PubMed

[2] W. M. Abd-Elhameed and Y. H. Youssri, Generalized Lucas polynomial sequence approach for fractional differential equations, Nonlinear Dyn. 89(2) (2017), 1341–1355.10.1007/s11071-017-3519-9Search in Google Scholar

[3] W. M. Abd-Elhameed and Y. H. Youssri, Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations, Comput. Appl. Math. 37(3) (2018), 2897–2921.10.1007/s40314-017-0488-zSearch in Google Scholar

[4] W. M. Abd-Elhameed and Y. H. Youssri, Spectral tau algorithm for certain coupled system of fractional differential equations via generalized Fibonacci polynomial sequence, Iran. J. Sci. Technol. Trans. A: Sci. 12 (2017), 1–12.10.1007/s40995-017-0420-9Search in Google Scholar

[5] M. Adel and M. M. Khader, Numerical simulation for studying the optimization problem as system of fractional differential equations using GEM, Appl. Math. 8 (2017), 1761–1768.10.4236/am.2017.812126Search in Google Scholar

[6] E. H. Doha, Y. H. Youssri and M. A. Zaky, Spectral solutions for differential and integral equations with varying coefficients using classical orthogonal polynomials, Bull. Iran. Math. Soc. 8(2) (2018), 1–29.10.1007/s41980-018-0147-1Search in Google Scholar

[7] E. H. Doha, Waleed M. Abd-Elhameed, Nermeen A. Elkot and Youssri H. Youssri, Integral spectral Tchebyshev approach for solving space Riemann-Liouville and Riesz fractional advection-dispersion problems, Adv. Differ. Equ. 2017(284) (2017), 1–23.10.1186/s13662-017-1336-6Search in Google Scholar

[8] R. M. Hafez and Y. H. Youssri, Jacobi collocation scheme for variable-order fractional reaction-subdiffusion equation, Comput. Appl. Math. 37(4) (2018), 5315–5333.10.1007/s40314-018-0633-3Search in Google Scholar

[9] M. M. Khader, On the numerical solutions for the fractional diffusion equation, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 2535–2542.10.1016/j.cnsns.2010.09.007Search in Google Scholar

[10] N. Bildik and S. Deniz, A new efficient method for solving delay differential equations and a comparison with other methods, Eur. Phys. J. Plus 132(51) (2017), 1–11.10.1140/epjp/i2017-11344-9Search in Google Scholar

[11] N. Bildik and S. Deniz, Comparative study between optimal homotopy asymptotic method and perturbation-iteration technique for different types of nonlinear equations, Iran. J. Sci. Tech., Trans. A: Sci. 42(2) (2018), 647–654.10.1007/s40995-016-0039-2Search in Google Scholar

[12] S. Deniz and N. Bildik, A new analytical technique for solving Lane-Emden type equations arising in astrophysics, Bull. Belgian Math. Soc.-Simon Stevin 24(2) (2017), 305–320.10.36045/bbms/1503453712Search in Google Scholar

[13] A. S. R. Kanth and P. M. M. Kumar, Numerical method for a class of nonlinear singularly perturbed delay differential equations using parametric cubic spline, Int. J. Nonl. Sci. Numer. Simul. 19(3) (2018), 357–366.10.1515/ijnsns-2017-0126Search in Google Scholar

[14] M. M. Khader and M. Adel, Numerical solutions of fractional wave equations using an efficient class of FDM based on the Hermite formula, Adv. Differ. Equ. (2012), doi: 10.1186/s13662-015-0731-0.Search in Google Scholar

[15] R. C. Mittal and S. Dahiya, A quintic B-spline based differential quadrature method for numerical solution of Kuramoto-Sivashinsky equation, Int. J. Nonlinear Sci. Numer. Simul. 8(2) (2017), 103–114.10.1515/ijnsns-2015-0190Search in Google Scholar

[16] N. H. Sweilam, M. M. Khader and M. Adel, Numerical simulation of fractional Cable equation of spiny neuronal dendrites, J. Adv. Res. (JAR) 5 (2014), 253–259.10.1016/j.jare.2013.03.006Search in Google Scholar PubMed PubMed Central

[17] N. H. Sweilam, M. M. Khader and M. Adel, Weighted average finite difference methods for fractional reaction-subdiffusion equation, Walailak J. Sci. Tech. 11(4) (2014), 361–377.Search in Google Scholar

[18] Y. H. Youssri and W. M. Abd-Elhameed, Numerical spectral Legendre-Galerkin algorithm for solving time fractional Telegraph equation, Rom. J. Phys. 63(107) (2018), 1–16.Search in Google Scholar

[19] Y. H. Youssri and W. M. Abd-Elhameed, Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials, Int. J. Opt. Control: Theor. Appl. 8(2) (2018), 152–160.10.11121/ijocta.01.2018.00442Search in Google Scholar

[20] E. Hanert, E. E. Schumacher and E. Deleersnijder, Front dynamics in fractional-order epidemic models, J. Theor. Bio. 279 (2011), 9–16.10.1016/j.jtbi.2011.03.012Search in Google Scholar PubMed

[21] E. Hanert, Front dynamics in a two-species competition model driven by Levy flights, J. Theor. Bio. 300 (2012), 134–142.10.1016/j.jtbi.2012.01.022Search in Google Scholar PubMed

[22] R. Kumar and S. Kumar, A new fractional modelling on Susceptible-Infected-Recovered equations with constant vaccination rate, Nonlinear Eng. 3(1) (2013), 11–19.10.1515/nleng-2013-0021Search in Google Scholar

[23] Z. M. Odibat and N. T. Shawagfeh, Generalized Taylor’s formula, Appl. Math. Comput. 186 (2007), 286–293.10.1016/j.amc.2006.07.102Search in Google Scholar

[24] W. Lin, Global existence theory and chaos control of fractional differential equations, J. Math. Anal. Appl. 332 (2007), 709–726.10.1016/j.jmaa.2006.10.040Search in Google Scholar

[25] D. Matignon, Stability results for fractional differential equations with applications to control processing, Computational Engineering in Systems and Application. In: Multiconference, IMACS, IEEE-SMC, Lille, France, 2 (1996), 963–968.Search in Google Scholar

[26] A. A. M. Arafa, S. Z. Rida and M. Khalil, Fractional modeling dynamics of HIV and CD4⁺ T-cells during primary infection, Nonlinear Biomed. Phys. 6(1) (2012), 1–7.10.1186/1753-4631-6-1Search in Google Scholar PubMed PubMed Central

[27] M. O. Zaid and S. Momani, An algorithm for the numerical solution of differential equations of fractional order, J. Appl. Math. Inf. 26 (2008), 15–27.Search in Google Scholar

[28] S. Side, A. M. Utami, Sukarna and M. I. Pratama, Numerical solution of SIR model for transmission of tuberculosis by Runge-Kutta method, IOP Conf. Series: J. Phys.: Conf. Series 1040 (2018) 012021, doi: 10.1088/1742-6596/1040/1/012021.Search in Google Scholar