| Keywords and phrases: biological population, fractional equation, Some Blaise Abbo (SBA) method, fractional partial differential equations (PDEs).
Received: September 7, 2023; Accepted: October 27, 2023; Published: January 9, 2024
How to cite this article: Bamogo Hamadou, Francis Bassono and Traoré André, Numerical resolution of the biological population model by the SBA method, Universal Journal of Mathematics and Mathematical Sciences 19(2) (2023), 119-137. http://dx.doi.org/10.17654/2277141723020
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References
[1] Abdoul Wassiha Nebie, Résolution de quelques équations fonctionnelles d’ordre fractionnaire au sens de Caputo par la méthode SBA et par la méthode HPM, Thèse de Doctorat unique, Université Joseph Ki-Zerbo, UFR SEA, 2022.
[2] Bamogo Hamadou, Francis Bassono, Yaya Moussa and Youssouf Paré, A new approach of SBA method for solving nonlinear fractional partial differential equations, International Journal of Numerical Methods and Applications 22 (2022), 117-137. http://dx.doi.org/10.17654/0975045222009
[3] Bamogo Hamadou, Francis Bassono, Kamaté Adama and Youssouf Paré, Analytical solution of some systems of nonlinear fractional differential equations by the SBA method, Journal of Mathematics Research 14(6) (2022), 13. https://doi.org/10.5539/jmr.v14n6p13.
[4] Béyi Boukary, Joseph Bonazebi-Yindoula, Justin Loufouilou-Mouyedo, Longin Some and Gabriel Bissanga, Application of the SBA method for solving partial differential equations, Nonlinear Analysis and Differential Equations 6(3) (2018), 91-103. https://doi.org/10.12988/nade.2018.866.
[5] Brahim Tellab, Résolution des équations différentielles fractionnaires, Thèse de Doctorat, Université Frères Mentouri Constantine 1, 2018.
[6] A. Burqan, A. Sarhan and R. Saadeh, Constructing analytical solutions of the fractional Riccati differential equations using Laplace residual power series method, Fractal Fract. 7 (2023), 14. https://doi.org/10.3390/fractalfract7010014.
[7] Francis Bassono, Résolution numérique comparée de quelques équations fonctionnelles par la méthode SBA, décompositionnelle d’Adomian et perturbation, Thèse de Doctorat unique, Université de Ouagadougou, UFR SEA, 2013.
[8] H. E. Roman and M. Giona, Fractional diffusion equation on fractals, J. Phys. A 25 (1992), 2107-2117.
[9] I. Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calc. Appl. Anal. 5 (2002), 367-386.
[10] Joseph Bonazebi Yindoula, Yanick Alain Servais Wellot, Bamogo Hamadou, Francis Bassono and Youssouf Paré, Application of the Some Blaise Abbo (SBA) method to solving the time-fractional Schrödinger equation and comparison with the homotopy perturbation method, Asian Research Journal of Mathematics 18(11) (2022), 271-286.
[11] Kamate Adama, Djibet Mbaiguesse, Bationo Jeremie Yiyureboula, Bakari Abbo and Youssouf Pare, Analytical solution of some nonlinear fractional integrodifferential equations of the Fredholm second kind by a new approximation technique of the numerical SBA method, International Journal of Numerical Methods and Applications 21 (2022), 37-58.
http://dx.doi.org/10.17654/0975045222003.
[12] MINOUGOU Youssouf, Contribution des méthodes SBA et Laplace-SBA à la resolution des modèles de convection-diffusion-réaction, Thèse de Doctorat Université Joseph Ki-Zerbo, 2019.
[13] Ouedraogo Seny, Abbo Bakari, Rasmane Yaro and Youssouf Pare, Convergence of a new approach of Adomian’s method for solving Volterra fractional integral of second kind, Far East J. Math. Sci. (FJMS) 127(2) (2020), 107-120.
[14] M. Partohaghighi, A. Akgül, E. K. Akgül, N. Attia, M. De la Sen and M. Bayram, Analysis of the fractional differential equations using two different methods, Symmetry 15 (2023), 65. https://doi.org/10.3390/sym15010065.
[15] Rasmané YARO, Contribution à la résolution de quelques équations fonctionnelles et modèles mathématiques de la dynamique des populations par les méthodes d’Adomian, SBA et des perturbations, Thèse de Doctorat unique, Université Joseph Ki-Zerbo, UFR SEA, 2016.
[16] Rawya AL-Deiakeh, Mohammed Ali, Marwan Alquran, Tukur A. Sulaiman, Shaher Momani and Mohammed AL-Smadi, On finding closed-form solutions to some nonlinear fractional systems via the combination of multi-Laplace transform and the Adomian decomposition method, Romanian Reports in Physics 74 (2022), 111.
[17] R. Sahadevan and T. Bakkyaraj, Invariant subspace method and exact solutions of certain nonlinear time fractional partial differential equations, Fract. Calc. Appl. Anal. 18 (2015), 146-162.
[18] Youssouf Pare, Resolution de quelques equations fonctionnelles par la numerique SBA (Some Blaise-Abbo), Thèse de Doctorat unique, Université de Ouagadougou, 2010.
[19] You ssouf Pare, Equations intégrales et intégro-différentielles, Generis Publishing, 2021.
[20] Stevy Mikamona Mayembo, Joseph Bonazebi-Yindoula, Youssouf Paré and Gabriel Bissanga, Application of the SBA method to solve the nonlinear biological population models, European Journal of Pure and Applied Mathematics 12(3) (2019), 1096-1105.
[21] Fatemeh Shakeri and Mehdi Dehghan, Numerical solution of a biological population model using He’s variational iteration method, Comput. Math. Appl. 54 (2007), 1197-1209.
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