Approximate analytical solution of time-fractional vibration equation via reliable numerical algorithm

AIMS Mathematics

article

M. Mossa Al-Sawalha¹  Azzh Saad Alshehry²  Kamsing Nonlaopon³  Rasool Shah⁴  Osama Y. Ababneh⁵ 

[1] Department of Mathematics, College of Science, University of Ha'il;Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University;Department of Mathematics, Faculty of Science, Khon Kaen University;Department of Mathematics, Abdul Wali khan university;Department of Mathematics, Faculty of Science, Zarqa University

关键词: homotopy perturbation method;    Adomian decomposition method;    Yang transform;    fractional vibration equation;    Caputo operator;   

DOI  :  10.3934/math.20221082

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY