SBA PLUS METHOD TO FIND SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER IN THE SENSE OF CAPUTO
Keywords:
Some Blaise Abbo (SBA) method, fractional functional equations, Caputo derivative, Riemann-Liouville integral, partial differential equations.DOI:
https://doi.org/10.17654/0975045224002Abstract
In this article, we focus on the solution of some nonlinear partial differential equations of fractional order in Caputo sense using the SBA plus method.
The SBA plus method is based on the combination of the Adomian decomposition method, Picard’s principle and the method of successive approximations. This method uses a process that converges rapidly to the exact solution, when it exists, in the function space, where the problem is posed.
Received: October 3, 2023
Accepted: November 10, 2023
References
A. Kadem and D. Baleanu, Méthode analytique basée sur la fonction de Walsh combinée à un polynôme orthogonal pour l’équation de transport fractionnaire, Commun. Nonlinear Sci. Numer. Simul. 15(3) (2010), 491-501.
A. Kadem and D. Baleanu, Homotopy perturbation method for the coupled fractional Lotka-Volterra equations, Rom. J. Phys. 56(3) (2011), 332-338.
A. Kadem and D. Baleanu, On fractional coupled Whitham-Broer-Kaup equations, Rom. J. Phys. 56(5) (2011), 629-635.
A. R. Nabulsi, The fractional white dwarf hydrodynamical nonlinear differential and emergence of quark stars, Appl. Math. Comput. 218(6) (2011), 2837-2849.
BENSID Ikram, Applications de la transformée de Laplace aux équations différentielles d’ordre non entier, Master’s thesis defended 13/10/2020, Université Larbi Ben M’hidi - Oum El Bouaghi, Algérie.
Blaise SOME, SBA method for solving mathematical models in the environment, European University Publishing, 2018.
BRAHIM Tellab. Résolution des équations différentielles fractionnaires, Thèse soutenue le 11/01/2018, Université des Frères Mentouri Constantine-1, Algérie.
B. Abbo, New numerical algorithm for solving ordinary differential equations (ODEs) and nonlinear partial differential equations (PDEs), Ph. D. Thesis, Université de Ouagadougou, UFR/SEA, Département Mathématique et Informatique (Burkina Faso), 2007.
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.
B. Zheng, -expansion method for solving fractional partial differential equations in the theory of mathematical physics, Commun. Theor. Phys. 58 (2012), 623-630.
Fatemeh Norouzi and Gaston M. N’Guérékata, A new study of fractional order financial system via homotopy analysis, Analele Universitatii Oradea, Fasc. Matematica, Tom XXVII(1) (2020), 141-152.
G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Math Comput. Modelling 13(7) (1990), 17-43.
Germain KABORE, KÉRÉ Moumini, Windjiré SOME, Ousséni SO and Blaise SOME, Solving some fractional equations, in the sense of Riemann-Liouville, of Navier-Stokes by the numerical method SBA plus, International Journal of Numerical Methods and Applications 23(2) (2023), 209-228.
http://dx.doi.org/10.17654/0975045223012.
Germain KABORE, Windjiré SOME, Moumini KÉRÉ, Ousséni SO and Blaise SOME, Solving some fractional ordinary differential equations by SBA method, Journal of Mathematics Research 15(1) (2023). doi :10.5539/jmr.v15n1pxx.
Houmor Tarek, Analyse du chaos dans un système d’équations différentielles fractionnaires, Thèse soutenue le 30/09/2014, Université Constantine 1, Algérie.
H. Jafari, A. Kadem, D. Baleanu and T. Yilmaz, Solutions of the fractional Davey-Stewartson equations with variational iteration method, Rom. Rep. Phys. 64(2) (2012), 337-346.
H. Jafari, A. Kadem, D. Baleanu and T. Yilmaz, Variational iteration method for a fractional-order Brusselator system, Abstr. Appl. Anal. (2014), 1-6, Article ID 496323.
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.
J. T. Katsikadelis, Nonlinear dynamic analysis of viscoelastic membranes described with fractional differential models, J. Theoret. Appl. Mech. 50(3) (2012), 743-753.
J. R. Wang and Y. Zhou, A class of fractional evolution equations and optimal controls, Nonlinear Anal. Real World Appl. 12 (2011), 262-272.
Mountassir Hamdi Cherif, Résolution numérique des équations différentielles et aux dérivées partielles non linéaire et d’ordre fractionnaire par la méthode HPM, Doctoral thesis defended on 17/05/2016, Université d’ORAN 1, AHMED BEN BELLA, Algérie.
NEFNAF Asma KERROUCHE Ibtissem, Résolution des équations différentielles partielles d’ordre fractionnaire moyennant des approches semi-analytique, Master’s thesis defended 07/07/2021, Université Mohamed El-Bachir El-Ibrahimi Bordj Bou Arréridj.
NSIMBA NDAMBA Higelin, Génération des solutions numériques pour certains types d’équations linéaires et non linéaires d’ordre fractionnaire, Mémoire de Master soutenue le 14 Janvier 2023, Université Marien NGOUABI, Congo Brazzaville.
Zaid Laadjal, Synchronisation des systèmes différentiels d’ordre entier et d’ordre fractionnaire, Mémoire de Master soutenue le 25/05/2017, Université de Larbi Tébéssi-Tébéssa, Algeria.
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