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September 2020 A new reliable method and its convergence for nonlinear second-order fractional differential equations
Ali Khalouta, Abdelouahab Kadem
Tbilisi Math. J. 13(3): 133-143 (September 2020). DOI: 10.32513/tbilisi/1601344903


The main goal of this article is to propose a new reliable method to solve nonlinear second-order fractional differential equations in particular, nonlinear fractional Bratu-type equation. This method called the modified Taylor fractional series method (MTFSM). The fractional derivative is defined in the Liouville-Caputo sense. Simplicity, rapid convergence, and high accuracy are the advantages of this method. In addition, the MTFSM reduces the size of calculations by not requiring linearization, discretization, perturbation or any other restriction. Three numerical examples are exhibited to demonstrate the reliability and efficiency of the proposed method, and the solutions are considered as an infinite series that converge rapidly to the exact solutions. The results display that the MTFSM is very effective and accurate to solve this type of nonlinear fractional problems.


The authors would like to thank Professor Hvedri Inassaridze (Editor-in-Chief) as well as the anonymous referees who has made valuable and careful comments, which improved the paper considerably.


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Ali Khalouta. Abdelouahab Kadem. "A new reliable method and its convergence for nonlinear second-order fractional differential equations." Tbilisi Math. J. 13 (3) 133 - 143, September 2020.


Received: 14 January 2020; Accepted: 5 August 2020; Published: September 2020
First available in Project Euclid: 29 September 2020

MathSciNet: MR4154839
Digital Object Identifier: 10.32513/tbilisi/1601344903

Primary: 34A08
Secondary: 26A33, 41A58, 74H15

Rights: Copyright © 2020 Tbilisi Centre for Mathematical Sciences


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Vol.13 • No. 3 • September 2020
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