Numerical solution the fractional Bagley–Torvik equation arising in fluid mechanics

References

• O. Abdulaziz, I. Hashim, and S. Momani, Solving systems of fractional differential equations by homotopy-perturbation method, Phys. Lett. A. 372 (2008), pp. 451–459. doi: 10.1016/j.physleta.2007.07.059
   Web of Science ®Google Scholar
• Q.M. Al-Mdallal, M.I. Syam, and M.N. Anwar, A collocation-shooting method for solving fractional boundary value problems, Commun. Nonlinear Sci. Numer. Simul. 15(12) (2010), pp. 3814–3822. doi: 10.1016/j.cnsns.2010.01.020
   Web of Science ®Google Scholar
• R.L. Bagley and P.J. Torvik, Fractional calculus in the transient analysis of viscoelastically damped structures, AIAA J. 23(6) (1985), pp. 918–925. doi: 10.2514/3.9007
   Google Scholar
• J. Deng and L. Ma, Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations, Appl. Math. Lett. 23 (2010), pp. 676–680. doi: 10.1016/j.aml.2010.02.007
   Web of Science ®Google Scholar
• K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag, Berlin Heidelberg, 2010.
   Google Scholar
• K. Diethelm and N.J. Ford, Numerical solution of the Bagley–Torvik equation, BIT 42 (2002), pp. 490–507.
   Web of Science ®Google Scholar
• K. Diethelm and N.J. Ford, Numerical solution of the Bagley–Torvik Equation, Swets Zeitlinger. 42(3) (2002), pp. 490–507.
   Google Scholar
• E.H. Doha, A.H. Bhrawy, and S.S. Ezz-Eldien, A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order, Comput. Math. Appl. 62 (2011), pp. 2364–2373. doi: 10.1016/j.camwa.2011.07.024
   Web of Science ®Google Scholar
• M. Gülsu and M. Sezer, A Taylor polynomial approach for solving differential difference equations, J. Comput. Appl. Math. 186 (2006), pp. 349–364. doi: 10.1016/j.cam.2005.02.009
   Web of Science ®Google Scholar
• Y. Hu, Y. Luo, and Z. Lu, Analytical solution of the linear fractional differential equation by Adomian decomposition method, J. Comput. Appl. Math. 215 (2008), pp. 220–229. doi: 10.1016/j.cam.2007.04.005
   Web of Science ®Google Scholar
• Y. Keskin, O. Karaoğlu, S. Servi, and G. Oturaç, The approximate solution of high order linear fractional differential equations with variable coefficients in terms of generalized Taylor polynomials, Math. Comput. Appl. 16(3) (2011), pp. 617–629.
   Google Scholar
• R. Lewandowski and B. Chorazyczewski, Identification of the parameters of the Kelvin–Voigt and the Maxwell fractional models, used to modeling of viscoelastic dampers, Comput. Struct. 88 (2010), pp. 1–17. doi: 10.1016/j.compstruc.2009.09.001
   Web of Science ®Google Scholar
• Y. Luchko and R. Gorenflo, An operational method for solving fractional differential equations with the Caputo derivatives, Acta Math. Vietnam. 24 (1999), pp. 207–233.
   Google Scholar
• K. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons Inc., New York, 1993.
   Google Scholar
• S. Momani and Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Solitons Fractals. 31 (2007), pp. 1248–1255. doi: 10.1016/j.chaos.2005.10.068
   Web of Science ®Google Scholar
• I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
   Google Scholar
• E.A. Rawashdeh, Numerical solution of fractional integro-differential equations by collocation method, Appl. Math. Comput. 176 (2006), pp. 1–6. doi: 10.1016/j.amc.2005.09.059
   Web of Science ®Google Scholar
• A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional order differential equations, Comput. Math. Appl. 59 (2010), pp. 1326–1336. doi: 10.1016/j.camwa.2009.07.006
   Web of Science ®Google Scholar
• S. Saha Ray, On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation, Appl. Math. Comput. 218 (2012), pp. 5239–5248. doi: 10.1016/j.amc.2011.11.007
   Web of Science ®Google Scholar
• P.J. Torvik and R.L. Bagley, On the appearance of the fractional derivative in the behavior of real materials, J. Appl. Mech. 51 (1984), pp. 294–298. doi: 10.1115/1.3167615
   Web of Science ®Google Scholar
• B.M. Vinagre, I. Podlubny, A. Hernandez, and V. Feliu, Some approximations of fractional operators used in control theory and applications, Fract. Calc. Appl. Anal. 3(3) (2000), pp. 945–950.
   Google Scholar