Lie symmetry analysis of a TFD system for transmission of HTVL virus type I to human CD4+ T-cells
*Mehdi NadjafikhahCorresponding authorm_nadjafikhah@iust.ac.irDepartment of Pure MathematicsSchool of MathematicsIran University of Science and TechnologyNarmak, Tehran, IranView full profile → , Hind Al-Bderihind.kadhum@qu.edu.iqDepartment of Financial and Banking SciencesCollege of Administration and EconomicsUniversity of Al-QadisiyahDiwaniyah, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Mar 2024
- Published Online:
- 30 Jun 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1918
- Pages:
- 975–990
Abstract
Keywords
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References
[1] H.I. Abdel-Gawad, M.S. Osman On the variational approach for analyzing the stability of solutions of evolution equations, Kyungpook Math. J. 53 4. 661–680 (2013).
[2] O.P. Agrawal, Formulation of Euler-Lagrange equations for fractional variational problems, J.Math. Anal. Appl 272 1, 12 pages (2002).
[3] K.K. Ali, M.A. Abd El Salam, E.M. H.Mohamed, B. Samet, S. Kumar, M.S. Osman, Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series, Adv. Differential Equations 494 (2020).
[4] G. Bluman, S.C. Anco, Symmetry and integration methods for differential equations, in: Applied Mathematical Sciences, Springer-Verlag, New York (2002).
[5] G.W. Bluman and S. Kumei. Symmetries and differential equations 81. Springer Science & Business Media (2013).
[6] B. Cuahutenango-Barro, M.A. Taneco-Hern’andez, Yu-Pei Lv, J.F. G’omez Aguilar, M.S. Osman, H. Jahanshahi, A.A. Aly, Analytical solutions of fractional wave equation with memory effect using the fractional derivative with exponential kernel, Results Phys. 25, 104148 (2021).
[7] K. Diethelm. The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. Springer Science & Business Media (2010).
[8] S. Djennadi, N. Shawagfeh, M. Inc, M.S. Osman, J.F. G’omez-Aguilar, O. Abu Arqub, The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique, Phys. Scr 96 9, 094006 (2020).
[9] V.D. Djordjevic, T.M. Atanackovic, Similarity solutions to nonlinear heat conduction and Burgers/Korteweg–deVries fractional equations, Comput. Appl. Math 222 2, 701–714 (2008).
[10] W.I. Fushchich, W.M. Shtelen, and N.I. Serov, Symmetry analysis and exact solutions of equations of nonlinear mathematical physics246 Springer Science & Business Media (2013).
[11] R.K. Gazizov, N.H. Ibragimov, S.Yu. Lukashchuk, Nonlinear self-adjointness, conservation laws and exact solutions of time-fractional Kompaneets equations, Commun Nonlinear Sci Numer Simulat 23, 153-163 (2015).
[12] R.K. Gazizov, A.A. Kasatkin, S.Y. Lukashchuk, Continuous transformation groups of fractional differential equations, Vestn. USATU 9, 125–135 (2007).
[13] N.H. Ibragimov and Vladimir F. Kovalev. Approximate and re norm group symmetries Springer Science & Business Media (2009).
[14] N.H. Ibragimov. Elementary Lie group analysis and ordinary differential equations. Wiley (1999).
[15] N.H. Ibragimov, A new conservation theorem, J Math Anal Appl 333, 311-328 (2007).
[16] G.F. Jefferson, J. Carminati, FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations, Computer Physics Communications 185, 430–441 (2014).
[17] G.F. Jefferson, J. Carminati, ASP: automated symbolic computation of approximate symmetries of differential equations, Computer Physics Communications 184, 1045–1063 (2013).
[18] G.F. Jefferson, J. Carminati, Finding generalised symmetries of differential equations using the MAPLE package DESOLVII, Computer Physics Communications 183, 1044–1054 (2012).
[19] S.Yu. Lukashchuk, Conservation laws for time-fractional subdiffusion and diffusion-wave equations, Nonlinear Dym 80, 791-802 (2015).
[20] S.V. Meleshko. Methods for constructing exact solutions of partial differential equations: mathematical and analytical techniques with applications to engineering. Springer Science & Business Media (2006).
[21] K.B. Oldham, F. Spanier. The Fractional Calculus, Academic Press, New York (1974).
[22] P.J. Olver. Applications of Lie groups to differential equations 107. Springer Science & Business Media (2012).
[23] M.S. Osman, Multiwave solutions of time-fractional (2+1)-dimensional Nizhnik–Novikov–Veselov equations, Pramana J. Phys 88 4, 67–75 (2017).
[24] C. Park, R.I. Nurudden, K.K. Ali, L. Muhammad, M.S. Osman, D. Baleanu, Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations, Adv. Differential Equations 627 (2020).
[25] I.Podlubny. Fractional Differential Equations.An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications, Academic Press, San Diego, CA (1999).
[26] N. Raza, M.S. Osman, A.H. Abdel-Aty, S. Abdel-Khalek, H.R. Besbes, Optical solitons of space–time fractional Fokas–Lenells equation with two versatile integration architectures, Adv. Differential Equations 517 (2020).
[27] F. Riewe, Mechanics with fractional derivatives, Phys. Rev E 55 3, 3581–3592 (1997).
[28] R. Sahadevan, P. Prakash, Exact solution of certain time fractional nonlinear partial differential equations, Nonlinear Dynam 85, 659–673, Springer (2016).
[29] Stilianakis NI, Seydel J., Modeling the T-cell dynamics and pathogenesis of HTLV-I infection. Bull Math Biol. 615935-47 (1999).
