.svg){kind=logo}
SOLUTIONS OF FRACTIONAL SCHRÖDINGER EQUATIONS IN THE CAPUTO SENSE USING SBA PLUS
Keywords:
Some Blaise Abbo method plus, Caputo’s fractional derivative, fractional Riemann-Liouville integral, PDE nonlinear of Schrödinger.DOI:
https://doi.org/10.17654/0972087124013Abstract
By the Some Blaise Abbo (SBA) plus method, we solve some nonlinear fractional time Schrödinger source problems of order $\alpha$ in the sense of Caputo in dimension one and also two. This method plays a decisive role in finding solutions to complex problems.
Received: February 28, 2024
Accepted: April 22, 2024
References
Blaise SOME, SBA Method for Solving Environmental Mathematical Models in the Environmental, European University Publications, 2018.
BRAHIM Tellab, Solving fractional differential equations, Constantine-1 Mentouri Brothers University, Thesis defended on 11/01/2018.
B. Abbo, Nouvel algorithme numérique de résolution des équations différentielles ordinaries (EDO) et des équations aux dérivées partielles (EDP) non linéaires, Thèse de Doctorat unique, Université de Ouagadougou, UFR/SEA, Département de 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, Annals of Oradea University, Fasc. Matematica, Tom XXVII(1) (2020), 141-152.
Christophe BESSE, Méthodes numériques et conditions aux limites artificielles pour les équations de Schrödinger linéaires et non linéaires et modélisation d’irrégularités du plasma ionosphérique terrestre, Université Paul Sabatier - Toulouse III, France, Thesis defended on 08/12/2004.
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), 47-56.
doi:10.5539/jmr.v15n1pxx.
Houmor Tarek, Chaos analysis in a system of fractional differential equations, Constantine 1 University, Thesis defended on 30/09/2014.
C. Besse, B. Bidégaray and S. Descombes, Order estimates in time of splitting methods for the nonlinear Schrödinger equation, SIAM J. Numer. Anal. 40(1) (2002), 26-40.
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.
Longin SOME, Moving grid method under the line method for the numerical resolution of partial differential equations modeling evolutionary phenomena, Doctoral thesis, University of Ouagadougou, Burkina Faso, 2007.
KEHAILI ABDELKADER, Numerical resolution of a certain type of partial equations of any order, University of DJILLALI LIABES, Algeria, Doctoral thesis, 2021.
BIEREBO Piercy Fare, Contribution to the solution of some partial integro differential equations of usual and fractional order by numerical methods ADM, SBA and its variants, University of MARIEN NGOUABI, Master’s degree, 2023.
NSIMBA NDAMBA Higelin, Numerical solution generation for certain types linear and nonlinear equations of fraction order, University of MARIEN NGOUAI, Congo, Master’s degree, 2023.
PARE YOUSSOUF, Resolution of some function equations by the numerical method SBA (Somé Blaise Abbo), University of Ouagadougou, Burkina Faso, Doctoral thesis, 2010.
MELIZI MERIEM, Numerical solutions of fractional order equations by the homotopic perturbation method, University Mohamed EL-Bachir EL-Ibrahimi of Bordj Bou Arréridj, Algeria, Master’s degree, 2023.
Lucie Baudouin, Contributions to the study of Schrödinger : inverse problem and bilinear optimal control Hartree-Fock equation, University of Versailles-Saint-Quentin, France, Doctoal thesis, 2004.
Nauman Raza and Muhammad Asad Ullah, A comparative study of the analyse of heat transfer of fractional Maxwell fluid using Caputo and Caputo-Fabrizio derivatives, Canadian Journal of Physics 98(1) (2020), 1-29.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
Contact Puspha Publishing House for more info or permissions.
