On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation

Abstract In the present analysis, the motion of an immersed plate in a Newtonian fluid described by Torvik and Bagley’s fractional differential equation [1] has been considered. This Bagley Torvik equation has been solved by operational matrix of Haar wavelet method. The obtained result is compared with analytical solution suggested by Podlubny [2] . Haar wavelet method is used because its computation is simple as it converts the problem into algebraic matrix equation.

[1]  Weiwei Zhao,et al.  Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations , 2010, Appl. Math. Comput..

[2]  R. Bagley,et al.  On the Appearance of the Fractional Derivative in the Behavior of Real Materials , 1984 .

[3]  P. Ruge,et al.  Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals , 2002 .

[4]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[5]  R. Gorenflo,et al.  Fractional Calculus: Integral and Differential Equations of Fractional Order , 2008, 0805.3823.

[6]  Adem Kiliçman,et al.  Kronecker operational matrices for fractional calculus and some applications , 2007, Appl. Math. Comput..

[7]  Mohamed Karim Bouafoura,et al.  PI λ D μ controller design for integer and fractional plants using piecewise orthogonal functions , 2010 .

[8]  Santanu Saha Ray,et al.  Analytical solution of the Bagley Torvik equation by Adomian decomposition method , 2005, Appl. Math. Comput..

[9]  I. Podlubny Fractional differential equations , 1998 .

[10]  H. Srivastava,et al.  THEORY AND APPLICATIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS. NORTH-HOLLAND MATHEMATICS STUDIES , 2006 .

[11]  Changrong Yi,et al.  Haar wavelet method for solving lumped and distributed-parameter systems , 1997 .

[12]  C. F. Chen,et al.  Haar wavelet method for solving lumped and distributed-parameter systems , 1997 .