2019
DOI: 10.1115/1.4043525
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A Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation

Abstract: We present a novel method to solve the Bagley-Torvik equation by transforming it into ordinary differential equations (ODEs). This method is based on the equivalence between the Caputo-type fractional derivative (FD) of order 3/2 and the solution of a diffusion equation subjected to certain initial and boundary conditions. The key procedure is to approximate the infinite boundary condition by a finite one, so that the diffusion equation can be solved by separation of variables. By this procedure, the Bagley-To… Show more

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Cited by 2 publications
(1 citation statement)
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“…Fitt et al [22] have also used it to deal with an engineering problem. Moreover, Xu et al [23] have used it reversely to transform the Bagley-Torvik equation into ordinary differential equations. We extend their method to solve the equation with time delay by transform it into delay defferential equations (DDEs).…”
Section: Introductionmentioning
confidence: 99%
“…Fitt et al [22] have also used it to deal with an engineering problem. Moreover, Xu et al [23] have used it reversely to transform the Bagley-Torvik equation into ordinary differential equations. We extend their method to solve the equation with time delay by transform it into delay defferential equations (DDEs).…”
Section: Introductionmentioning
confidence: 99%