@article{Al-Sawalha2022, 
author = {M. Mossa Al-Sawalha and Azzh Saad Alshehry and Kamsing Nonlaopon and Rasool Shah and Osama Y. Ababneh},
title = {Approximate analytical solution of time-fractional vibration equation via reliable numerical algorithm},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {11},
pages = {19739-19757},
keywords = {homotopy perturbation method, Adomian decomposition method, Yang transform, fractional vibration equation, Caputo operator},
url = {https://www.sciopen.com/article/10.3934/math.20221082},
doi = {10.3934/math.20221082},
abstract = {With effective techniques like the homotopy perturbation approach and the Adomian decomposition method via the Yang transform, the time-fractional vibration equation's solution is found for large membranes. In Caputo's sense, the fractional derivative is taken. Numerical experiments with various initial conditions are carried out through a few test examples. The findings are described using various wave velocity values. The outcomes demonstrate the competence and reliability of this analytical framework. Figures are used to discuss the solution of the fractional vibration equation using the suggested strategies for different orders of memory-dependent derivative. The suggested approaches reduce computation size and time even when the accurate solution of a nonlinear differential equation is unknown. It is helpful for both small and large parameters. The results show that the suggested techniques are trustworthy, accurate, appealing and effective strategies.}
}