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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Published in:AIMS mathematics Vol. 7; no. 11; pp. 19739 - 19757
Main Authors: Al-Sawalha, M. Mossa, Alshehry, Azzh Saad, Nonlaopon, Kamsing, Shah, Rasool, Ababneh, Osama Y.
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2022
Subjects:
adomian decomposition method
caputo operator
fractional vibration equation
homotopy perturbation method
yang transform
ISSN:2473-6988, 2473-6988
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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.
AbstractList 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.
Author Ababneh, Osama Y.
Nonlaopon, Kamsing
Alshehry, Azzh Saad
Al-Sawalha, M. Mossa
Shah, Rasool
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  organization: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
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Snippet With effective techniques like the homotopy perturbation approach and the Adomian decomposition method via the Yang transform, the time-fractional vibration...
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SubjectTerms adomian decomposition method
caputo operator
fractional vibration equation
homotopy perturbation method
yang transform
Title Approximate analytical solution of time-fractional vibration equation via reliable numerical algorithm
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