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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 this 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 = xα , 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

Bagley-Torvik equation, fractional derivative, Galerkin method, numerical solutions.

Cite This Article

Yüzbaşı, Ş., Karaçayır, M. (2020). A Galerkin-Type Fractional Approach for Solutions of Bagley-Torvik Equations. CMES-Computer Modeling in Engineering & Sciences, 123(3), 941–956.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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