Geodesic
A new application of Khalouta differential transform method and
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 2, pp. 207-222

Voir la notice de l'article provenant de la source Math-Net.Ru

In this study, we propose a new hybrid numerical method called the Khalouta differential transform method to solve the nonlinear fractional Liénard equation involving the Caputo fractional derivative. The convergence theorem of the proposed method is proved under suitable conditions. The Khalouta differential transform method is a semi-analytical technique that combines two powerful methods: the Khalouta transform method and the differential transform method. The main advantage of this approach is that it provides very fast solutions without requiring linearization, perturbation, or any other assumptions. The proposed method is described and illustrated with two numerical examples. The illustrative examples show that the numerical results obtained are in very good agreement with the exact solutions. This confirms the accuracy and effectiveness of the proposed method.
Keywords: Caputo fractional derivative, differential transform method, approximate solution
Mots-clés : fractional Liénard equation, Khalouta transform method 
@article{VSGTU_2024_28_2_a0,
     author = {L. Chetioui and A. Khalouta},
     title = {A new application of {Khalouta} differential transform method and},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {207--222},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2024_28_2_a0/}
}
TY  - JOUR
AU  - L. Chetioui
AU  - A. Khalouta
TI  - A new application of Khalouta differential transform method and
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2024
SP  - 207
EP  - 222
VL  - 28
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2024_28_2_a0/
LA  - en
ID  - VSGTU_2024_28_2_a0
ER  - 
%0 Journal Article
%A L. Chetioui
%A A. Khalouta
%T A new application of Khalouta differential transform method and
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2024
%P 207-222
%V 28
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2024_28_2_a0/
%G en
%F VSGTU_2024_28_2_a0
L. Chetioui; A. Khalouta. A new application of Khalouta differential transform method and. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 2, pp. 207-222. http://geodesic.mathdoc.fr/item/VSGTU_2024_28_2_a0/