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

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 v...

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Vydáno v:AIMS mathematics Ročník 7; číslo 11; s. 19739 - 19757
Hlavní autoři: Al-Sawalha, M. Mossa, Alshehry, Azzh Saad, Nonlaopon, Kamsing, Shah, Rasool, Ababneh, Osama Y.
Médium: Journal Article
Jazyk:angličtina
Vydáno: AIMS Press 01.01.2022
Témata:
adomian decomposition method
caputo operator
fractional vibration equation
homotopy perturbation method
yang transform
ISSN:2473-6988, 2473-6988
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Shrnutí: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20221082