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Volume 16, Issue 2 (2024) , Pages [135] - [211]
ON VARIATIONAL ITERATION METHODS FOR THE FRACTIONAL MODEL OF BLOOD ETHANOL CONCENTRATION SYSTEM
[1] M. Adel, M. M. Khader, H. Ahmad and T. A. Assiri, Approximate analytical solutions for the blood ethanol concentration system and predator-prey equations by using variational iteration method, AIMS Mathematics 8(8) (2023), 19083-19096.
DOI: https://doi.org/10.3934/math.2023974
[2] A. A. M. Arafa and A. M. SH. Hagaga, A new analytic solution of fractional coupled Ramani equation, Chinese Journal of Physics 60 (2019), 388-406.
DOI: https://doi.org/10.1016/j.cjph.2019.05.011
[3] A. A. M. Arafa, M. Khalil and A. Sayed, A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay, Hindawi, Complexity (2019), 13 pp.
DOI: https://doi.org/10.1155/2019/4291017
[4] D. Bravo, M. Barrios and G. Reyero, Analysis of a fractional-order predator-prey model with harvest incorporating an Allee effect, Journal of Fractional Calculus and Applications 14(2) (2023), 14 pp.
DOI: https://doi.org/10.21608/jfca.2023.204624.1010
[5] M. Bohner, O. Tunç and C. Tunç, Qualitative analysis of caputo fractional integro-differential equations with constant delays, Computational and Applied Mathematics 40(6) (2021); Article 214.
DOI: https://doi.org/10.1007/s40314-021-01595-3
[6] M. A. Cohen, Numerical Methods for Laplace Transform Inversion, Numerical Methods and Algorithms, Springer,
DOI:https://doi.org/10.1007/978-0-387-68855-8
[7] K. Diethelm, J. Ford, N. Ford and M. Weilbeer, Pitfalls in fast numerical solvers for fractional differential equations, Journal of Computational and Applied Mathematics 186(2) (2006), 482-503.
DOI: https://doi.org/10.1016/j.cam.2005.03.023
[8] A. M. A. El-Sayed, A. A. M. Arafa, M. Khalil and A. Hassan, A mathematical model with memory for propagation of computer virus under human intervention, Progress in Fractional Differentiation and Applications 2(2) (2016), 105-113.
DOI: https://doi.org/10.18576/pfda/020203
[9] S. El-Wakil, E. Abulwafa, E. El-Shewy and A. Mahmoud, Ion-acoustic waves in unmagnetized collisionless weakly relativistic plasma of warm-ion and isothermal-electron using time-fractional KdV equation, Advances in Space Research 49(12) (2012), 1721-1727.
DOI: https://doi.org/10.1016/j.asr.2012.02.018
[10] V. Ertürk, Z. Odibat and
DOI: https://doi.org/10.1016/j.camwa.2011.03.091
[11] S. Esmaeili, M. Shamsi and Y. Luchko, Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials, Computers & Mathematics with Applications 62(3) (2011), 918-929.
DOI: https://doi.org/10.1016/j.camwa.2011.04.023
[12] N. Ford and J. Connolly, Comparison of numerical methods for fractional differential equations, Communications on Pure and Applied Analysis 5(2) (2006), 289-307.
DOI: https://doi.org/10.3934/cpaa.2006.5.289
[13] F. Ghoreishi and S. Yazdani, An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis, Computers & Mathematics with Applications 61(1) (2011), 30-43.
DOI: https://doi.org/10.1016/j.camwa.2010.10.027
[14] R. Gorenflo and F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, Fractals and Fractional Calculus, Carpinteri and
[15] H. Jafari, S. Das and H. Tajadodi, Solving a multi-order fractional differential equation using homotopy analysis method, Journal of King Saud University - Science 23(2) (2011), 151-155.
DOI: https://doi.org/10.1016/j.jksus.2010.06.023
[16] H. Jafari, H. Tajadodi and D. Baleanu, A modified variational iteration method for solving fractional Riccatti differential equation by Adomian polynomials, Fractional Calculus and Applied Analysis 16(1) (2013), 109-122.
DOI: https://doi.org/10.2478/s13540-013-0008-9
[17] M. Johansyah, A. Supriatna, E. Rusyaman and J. Saputra, Application of fractional differential equation in economic growth model: A systematic review approach, AIMS Mathematics 6(9) (2021), 10266-10280.
DOI: https://doi.org/10.3934/math.2021594
[18] Y. Khan, N. Faraz, A. Yildirim and Q. Wu, Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science, Computers & Mathematics with Applications 62(5) (2011), 2273-2278.
DOI: https://doi.org/10.1016/j.camwa.2011.07.014
[19] V. Krishnasamy, S. Mashayekhi and M. Razzaghi, Numerical solutions of fractional differential equations by using fractional Taylor basis, IEEE/CAA Journal of Automatica Sinica 4(1) (2017), 98-106.
DOI: https://doi.org/10.1109/JAS.2017.7510337
[20] C. Li and Y. Wang, Numerical algorithm based on Adomian decomposition for fractional differential equations, Computers & Mathematics with Applications 57(10) (2009), 1672-1681.
DOI: https://doi.org/10.1016/j.camwa.2009.03.079
[21] C. Li and F. Zeng, Finite difference methods for fractional differential equations, International Journal of Bifurcation and Chaos 22(4) (2012), 1230014.
DOI: https://doi.org/10.1142/S0218127412300145
[22] Y. Luchko and R. Gorenflo, An operational method for solving fractional differential equations with the Caputo derivatives, Acta Mathematica Vietnamica 24(2) (1999), 207-233.
[23] S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, USA, 1993.
[24] S. Momani and Z. Odibat, Numerical approach to differential equations of fractional order, Journal of Computational and Applied Mathematics 207(1) (2007), 96-110.
DOI: https://doi.org/10.1016/j.cam.2006.07.015
[25] S. Momani and Z. Odibat, The variational iteration method: An efficient scheme for handling fractional partial differential equations in fluid mechanics, Computers & Mathematics with Applications 58(11-12) (2009), 2199-2208.
DOI: https://doi.org/10.1016/j.camwa.2009.03.009
[26] G. Monzón, On numerical approximation of second-order fractional differential equations in the frame of the Caputo fractional derivative, Journal of Fractional Calculus and Applications 14(1) (2023), 200-213.
[27] G. Monzón, Fractional variational iteration method for higher-order fractional differential equations, Journal of Fractional Calculus and Applications 15(1) (2024), 15 pp.
DOI: https://doi.org/10.21608/jfca.2023.229366.1027
[28] K. Oldham, Fractional differential equations in electrochemistry, Advances in Engineering Software 41(1) (2010), 9-12.
DOI: https://doi.org/10.1016/j.advengsoft.2008.12.012
[29] A. Prakash, M. Goyal and
DOI: https://doi.org/10.1515/nleng-2018-0001
[30] S. Qureshi, A. Yusuf, A. A. Shaikh, M. Inc and D. Baleanu, Fractional modeling of blood ethanol concentration system with real data application, Chaos 29(1) (2019); Article 013143.
DOI: https://doi.org/10.1063/1.5082907
[31] A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional-order differential equations, Computers & Mathematics with Applications 59(3) (2010), 1326-1336.
DOI: https://doi.org/10.1016/j.camwa.2009.07.006
[32] B. Si-yuan, Fractional variational iteration method for fractional Cauchy problems, Mathematical Problems in Engineering 4 (2014), 1-5.
DOI: https://doi.org/10.1155/2014/925016
[33] O. Tunç and C. Tunç, Solution estimates to Caputo proportional fractional derivative delay integro-differential equations, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales: Serie A. Matemáticas 117 (2023), 12.
DOI: https://doi.org/10.1007/s13398-022-01345-y
[34] G.-C. Wu, A fractional variational iteration method for solving fractional nonlinear differential equations, Computers & Mathematics with Applications 61(8) (2011), 2186-2190.
DOI: https://doi.org/10.1016/j.camwa.2010.09.010
[35] G.-C. Wu and D. Baleanu, Variational iteration method for fractional calculus - A universal approach by
DOI: https://doi.org/10.1186/1687-1847-2013-18
[36] Z. U. A. Zafar, S. Zaib, M. T. Hussain, C. Tunç and S. Javeed, Analysis and numerical simulation of tuberculosis model using different fractional derivatives, Chaos, Solitons & Fractals 160 (2022), 12 pp; Article 112202.