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Reliable analysis for the nonlinear fractional calculus model of the semilunar heart valve vibrations
Author(s) -
Yıldırım Ahmet,
Gülkanat Yaǧmur
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1399
Subject(s) - fractional calculus , laplace transform , linearization , homotopy analysis method , nonlinear system , vibration , mathematics , homotopy perturbation method , perturbation (astronomy) , mathematical analysis , homotopy , convergent series , calculus (dental) , physics , pure mathematics , medicine , dentistry , quantum mechanics , power series
Abstract The aim of this paper is to solve the equation of motion of semilunar heart valve vibrations using the homotopy perturbation method. The vibrations of the closed semilunar valves were modeled with fractional derivatives. The fractional derivatives are described in the Caputo sense. The methods give an analytic solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. Analytical solution is obtained for the equation of motion in terms of Mittag–Leffler function with the help of Laplace transformation. These solutions can be interesting for a better fit of experimental data. Copyright © 2010 John Wiley & Sons, Ltd.