Application of the Some Blaise Abbo (SBA) Method to Solving the Time-fractional Schrödinger Equation and Comparison with the Homotopy Perturbation Method
Joseph Bonazebi Yindoula
Marien M’Gouabi University, Congo.
Yanick Alain Servais Wellot
Marien M’Gouabi University, Congo.
Bamogo Hamadou
Joseph Ki-Zerbo University, Burkina Faso.
Francis Bassono
Joseph Ki-Zerbo University, Burkina Faso.
Youssouf Paré *
Joseph Ki-Zerbo University, Burkina Faso.
*Author to whom correspondence should be addressed.
Abstract
We have solved the Schrödinger equation with the HPM method and the SBA method. We have noticed that with these two methods we find the same result.
Keywords: Fractional equation, Some Blaise Abbo (SBA) method, the Homotopy Perturbation Method (HPM), Schrödinger equation, fractional Partial Differential Equations (PDEs)
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References
Wazwaz AM. A study on linear and nonlinear Schrödinger Equation by the variational iteration method. Chaos, Solitons and Fractals. 2008;37:1136-1142.
Ravi Kanth ASV, Aruna K. Two dimensional diferential transform method for solving linear and non-linear Schrödinger Equation, Chaos, Solitons and Fractals. 2009;41:2277-2281.
Golmankhaneh AK, Ali K. Golmankhaneh. Homotopy perturbation method for solving a system of Schrödinger-korteweg de vries, equation. Romanian Reports in Physics. 2011;63:609- 623.
Khan NA, Jamil M, Ara A. Approximate solution to Time Fractional Schrödinger Equation via Homotopy analysis method. ISRN Mathematical Physics; 2012, Article ID 197068, 11 pages.
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, Soutenue le 11 mars 2022, UFR SEA.
Ouedraogo Seny, Abbo Bakari, Rasmane Yaro and Youssouf Paré. Convergence of a new approach of Adomian’s method for solving volterra fractional integral of second kind. 2020;127(2):107-120.
Brahim Tellab. Résolution des équations différentielles fractionnaires, Thèse de doctorat, Université des Frères Mentouri Constantine-1 soutenu le 11-01-2018.
Youssouf Paré. Equations intégrales et intégro-différentielles. Generis Publishing; 2021.
Mahdy AMS, Mohamed AS, Mtawal AAH. Variational homotopy perturbation method for solving the generalized time-space fractional Schrödinger equation. International Journal of Physical Science. 2015;10(11):342-350.
Mtawal AAH, Alkaleeli SR, Mtawal AAH. A new modified homotopy perturbation method for fractional partial differential equations with proportional delay. Journal of Advances in Mathematics. 2020;19:58-73.
Mahdy AMS, Mohamed AS, Mtawal AAH. Implementation of the homotopy perturbation sumudu transform method for solving Klein-Gordon equation. Applied Mathematics. 2015;6(03):617-628.