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Kabore, Germain; Moumini, Kéré; Some, Windjiré; So, Ousséni; Some, Blaise

Solving some fractional equations, in the sense of Riemann-Liouville, of Navier-Stokes by the numerical method SBA plus. (English) Zbl 07835815

Int. J. Numer. Methods Appl. 23, No. 2, 209-228 (2023).

Cited in 3 Documents

MSC:

65Nxx Numerical methods for partial differential equations, boundary value problems
65Lxx Numerical methods for ordinary differential equations
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65Qxx Numerical methods for difference and functional equations, recurrence relations

Keywords:

Some Blaise Abbo (SBA) plus method; fractional functional equations; Riemann-Liouville derivative; Navier-Stokes equations
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Full Text: DOI

References:

[1] A. A. Ragab, K. M. Hemida, M. S. Mohamed, M. A. El Salam and N. City, Solution of time-fractional Navier-Stokes equation by using homotopy analysis method, Gen. Math. Notes 13(2) (2012), 13-21.
[2] Abdoul Wassiha NEBIE, Frédéric BERE, Bakari ABBO and Youssouf PARE, Solving some derivative equations fractional order nonlinear partials using the Some Blaise Abbo method, Journal of Mathematics Research 13(2) (2021), 101-115.
[3] A. Kadem and D. Baleanu, Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation, Commun. Nonlinear Sci. Numer. Simul. 15(3) (2010), 491-501. · Zbl 1221.45008
[4] A. Kadem and D. Baleanu, Homotopy perturbation method for the coupled fractional Lotka-Volterra equations, Rom. J. Phys. 56(3) (2011), 332-338. · Zbl 1231.65134
[5] A. Kadem and D. Baleanu, On fractional coupled Whitham-Broer-Kaup equations, Rom. J. Phys. 56(5) (2011), 629-635. · Zbl 1231.35203
[6] G. KABORE, K. Moumini, W. SOME, O. SO and B. SOME 226
[7] B. Abbo, O. SO, G. BARRO and B. SOME, A new numerical algorithm for solving nonlinear partial differential equations with initial and boundary conditions, Far East J. Appl. Math. 28(1) (2007), 37-52. · Zbl 1132.65095
[8] Kamate Adama, Bationo Jeremie Yiyureboula, Djibet Mbaiguesse and Youssouf Pare, Analytical solutions of classical and fractional Navier-Stokes equations by the SBA method, Journal of Mathematics Research 14(4) (2022). · Zbl 1513.65507
[9] https://doi.org/10.5539/jmr.v14n4p20. · doi:10.5539/jmr.v14n4p20
[10] A. Khalouta and A. Kadem, A new numérical technique for solving caputo time-fractional biological population equation, AIMS Mathematics 4(5) (2019), 1307-1319. · Zbl 1486.65218
[11] A. R. Nabulsi, The fractional white dwarf hydrodynamical nonlinear differential and emergence of quark stars, Appl. Math. Comput. 218(6) (2011), 2837-2849. · Zbl 1243.85006
[12] Blaise SOME, Méthode SBA de résolution des modèles mathématiques en environnement, Éditions Universitaires Européennes, 2018.
[13] B. Abbo, Nouvel algorithme numérique de résolution des équations différentielles ordinaires (EDO) et des équations aux dérivées partielles (EDP) non linéaires, Thèse de Doctorat unique, Université de Ouagadougou, UFR/ SEA, Département Mathématique et Informatique (Burkina Faso), 2007.
[14] B. Zheng, (
[15] G G′ -expansion method for solving fractional partial differential equations in the theory of mathematical physics, Commun. Theor. Phys. 58 (2012), 623-630. · Zbl 1264.35273
[16] D. Kumar, J. Singh and S. Kumar, A fractional model of Navier-Stokes equation arising in unsteady flow of a viscous fluid, J. Assoc. Arab Univ. Basic Appl. Sci. 17(1) (2015), 14-19.
[17] E. S. Moustafa and S. Ahmed, On the generalized Navier-Stokes equations, J. Appl. Math. Comput. 156(1) (2004), 287-293. · Zbl 1134.76323
[18] G. KABORE, W. Some, M. KÉRÉ, O. SO and B. SOME, Solving some fractional ordinary differential equations by SBA method, Journal of Mathematical Research 15(1) (2023), 47. Doi:10.5539/jmr.v15n1p47. · doi:10.5539/jmr.v15n1p47
[19] G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Math. Comput. Modelling 13(7) (1990), 17-43. · Zbl 0713.65051
[20] G. A. Birajdar, Numerical solution of time fractional Navier-Stokes equation by discrete Adomian decomposition method, Nonlinear Eng. 3(1) (2014), 21-26.
[21] Solving Some Fractional Equations, in the Sense … 227
[22] J. Singh, D. Kumar and A. Kilicman, Numerical solutions of nonlinear, fractional partial differential equations arising in spatial diffusion of biological populations, Abstr. Appl. Anal. 2014, Article ID 535793, 1-12. · Zbl 1474.65415
[23] J. T. Katsikadelis, Nonlinear dynamic analysis of viscoelastic membranes described with fractional differential models, J. Theoret. Appl. Mech. 50(3) (2012), 743-753.
[24] J. R. Wang and Y. Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal. Real World Appl. 12 (2011), 262-272. · Zbl 1214.34010
[25] K. Abbaoui, Les fondements de la méthode décompositionnelle d’Adomian et application à la résolution de problèmes issus de la biologie et de la médecine, Thèse de Doctorat de l’université Paris VI, 1995.
[26] Olivier Botella, Résolution des équations de Navier-Stokes par des schémas de projection Tchebychev, INRIA, 1996. inria-00073676.
[27] Rasool Shah, Hassan Khan, Dumitru Baleanu, Poom Kunam and Muhammad Arif, The Analytical Investigation of Time-fractional Multi-dimensional Navier-Stokes Equation, Elsevier, 2020. https://doi.org/10.1016/j.aej.2020.03.029 · Zbl 1485.65109 · doi:10.1016/j.aej.2020.03.029
[28] R. Herrmann, Fractional Calculus: An Introduction for Physicists, Word Scientific, 2011. · Zbl 1232.26006
[29] R. Herrmann, Applications of Fractional Calculus in Physics, Word Scientific, Singapore, 2000. · Zbl 0998.26002
[30] S. Kumar, D. Kumar, S. Abbasbandy and M. M. Rashidi, Analytical solution of fractional Navier-Stokes equation by using modified Laplace decomposition method, Ain Shams Eng. J. 5(2) (2014), 569-574.
[31] S. Momani and Z. Odibat, Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method, Appl. Math. Comput. 177(2) (2006), 488-494. · Zbl 1096.65131
[32] V. B. L. Chaurasia and D. Kumar, Solution of the time-fractional Navier-Stokes equation, Gen. Math. Notes 4(2) (2011), 49-59.
[33] Y. Cherruault, G. Saccomandi and B. Somé, News results for convergence of Adomian’s method applied to integral equations, Math. Comput. Modelling 16(2) (1992), 85-93. · Zbl 0756.65083
[34] G. KABORE, K. Moumini, W. SOME, O. SO and B. SOME 228
[35] Zoubir DAHMANI and Ahmed ANBER, The variational iteration method for solving the fractional foam drainage equation, International Journal of Nonlinear Science 10(1) (2010), 39-45. · Zbl 1226.35082
[36] Z. Odibat and S. Momani, The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics, Comput. Math. Appl. 58 (2009), 2199-2208. · Zbl 1189.65254
[37] Z. Z. Ganji, D. D. Ganji, A. D. Ganji and M. Rostamian, Analytical solution of time-fractional Navier-Stokes equation in polar coordinate by homotopy perturbation method, Numer. Methods Partial Differential Equations 26(1) (2010), 117-124. · Zbl 1423.35396
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