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ARTICLE

A Galerkin-Type Fractional Approach for Solutions of Bagley-Torvik Equations

Şuayip Yüzbaşı^{1, *}, 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.

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Citations