# Numerical Solution of the Bagley-Torvik Equation Using the Integer-Order Derivatives Expansion

• Afrah S. Hasan University of Duhok
Keywords: Bagley-Torvik Equation, Riemann–Liouville Fractional Integral and Derivative, Numerical Solution, Infinite Series of Integer-Order Derivative Expansion

### Abstract

Numerical solution of the well-known Bagley-Torvik equation is considered. The fractional-order derivative in the equation is converted, approximately, to ordinary-order derivatives up to second order. Approximated Bagley-Torvik equation is obtained using finite number of terms from the infinite series of integer-order derivatives expansion for the Riemann–Liouville fractional derivative. The Bagley-Torvik equation is a second-order differential equation with constant coefficients. The derived equation, by considering only the first three terms from the infinite series to become a second-order ordinary differential equation with variable coefficients, is numerically solved after it is transformed into a system of first-order ordinary differential equations. The approximation of fractional-order derivative and the order of the truncated error are illustrated through some examples. Comparison between our result and exact analytical solution are made by considering an example with known analytical solution to show the preciseness of our proposed approach.

### Author Biography

Afrah S. Hasan, University of Duhok

Department of Mathematics, Faculty of Science, University of Duhok.

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Published
2018-06-30
How to Cite
Hasan, A. (2018). Numerical Solution of the Bagley-Torvik Equation Using the Integer-Order Derivatives Expansion. Science Journal of University of Zakho, 6(2), 64-69. https://doi.org/10.25271/2018.6.2.437
Section
Science Journal of University of Zakho