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ARTICLE
A Galerkin-Type Fractional Approach for Solutions of Bagley-Torvik Equations
Şuayip Yüzbaşı1, *, Murat Karaçayır1
1 Department of Mathematics, Akdeniz University, Antalya, 07070, Turkey.
* Corresponding Author: Şuayip Yüzbaşı. Email: .
(This article belongs to the Special Issue: Numerical Methods for Differential and Integral Equations)
Computer Modeling in Engineering & Sciences 2020, 123(3), 941-956. https://doi.org/10.32604/cmes.2020.08938
Received 26 October 2019; Accepted 07 January 2020; Issue published 28 May 2020
Abstract
In this study, we present a numerical scheme similar to the Galerkin method in
order to obtain numerical solutions of the Bagley Torvik equation of fractional order 3/2. In
this approach, the approximate solution is assumed to have the form of a polynomial in the
variable t = x
α
, where α is a positive real parameter of our choice. The problem is firstly
expressed in vectoral form via substituting the matrix counterparts of the terms present
in the equation. After taking inner product of this vector with nonnegative integer powers
of
t up to a selected positive parameter
N, a set of linear algebraic equations is obtained.
After incorporation of the boundary conditions, the approximate solution of the problem
is then computed from the solution of this linear system. The present method is illustrated
with two examples.
Keywords
Cite This Article
APA Style
Yüzbaşı, Ş., Karaçayır, M. (2020). A galerkin-type fractional approach for solutions of bagley-torvik equations. Computer Modeling in Engineering & Sciences, 123(3), 941-956. https://doi.org/10.32604/cmes.2020.08938
Vancouver Style
Yüzbaşı Ş, Karaçayır M. A galerkin-type fractional approach for solutions of bagley-torvik equations. Comput Model Eng Sci. 2020;123(3):941-956 https://doi.org/10.32604/cmes.2020.08938
IEEE Style
Ş. Yüzbaşı and M. Karaçayır, "A Galerkin-Type Fractional Approach for Solutions of Bagley-Torvik Equations," Comput. Model. Eng. Sci., vol. 123, no. 3, pp. 941-956. 2020. https://doi.org/10.32604/cmes.2020.08938
Citations