Numerical approach for solving fractional Fredholm integro-differential equation

In this article, we present a new method which is based on the Taylor Matrix Method to give approximate solution of the linear fractional Fredholm integro-differential equations. This method is based on first taking the truncated Taylor expansions of the functions in the linear fractional differential part and Fredholm integral part then, substituting their matrix forms into the equation. We solve this matrix equation with the assistance of Maple 13. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method.

[1]  I. Ozkol,et al.  Solution of fractional integro-differential equations by using fractional differential transform method , 2009 .

[2]  Zaid M. Odibat,et al.  Generalized Taylor's formula , 2007, Appl. Math. Comput..

[3]  Mohsen Razzaghi,et al.  The Legendre wavelets operational matrix of integration , 2001, Int. J. Syst. Sci..

[4]  Aytac Arikoglu,et al.  Solution of fractional differential equations by using differential transform method , 2007 .

[5]  Mehmet Sezer,et al.  The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials , 2000, Appl. Math. Comput..

[6]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[7]  Ning Sun,et al.  Numerical solution of fractional differential equations using the generalized block pulse operational matrix , 2011, Comput. Math. Appl..

[8]  Mehmet Sezer,et al.  A new collocation method for solution of mixed linear integro-differential-difference equations , 2010, Appl. Math. Comput..

[9]  G. Adomian.  A review of the decomposition method in applied mathematics , 1988 .

[10]  Yildiray Keskin,et al.  The Approximate Solution of High-Order Linear Fractional Differential Equations with Variable Coefficients in Terms of Generalized Taylor Polynomials , 2011 .

[11]  Khosrow Maleknejad,et al.  Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions , 2004, Appl. Math. Comput..

[12]  Guy Jumarie,et al.  Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker–Planck equations , 2004 .

[13]  Mehmet Sezer,et al.  Approximations to the solution of linear Fredholm integrodifferential-difference equation of high order , 2006, J. Frankl. Inst..

[14]  Saeed Kazem,et al.  A novel application of radial basis functions for solving a model of first-order integro-ordinary differential equation , 2011 .

[15]  Esmail Babolian,et al.  Numerical solution of linear integro-differential equation by using sine-cosine wavelets , 2006, Appl. Math. Comput..

[16]  Reyad El-Khazali,et al.  Fractional-order dynamical models of love , 2007 .

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

[18]  Zhengyi Lu,et al.  Analytical solution of the linear fractional differential equation by Adomian decomposition method , 2008 .

[19]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[20]  N. Ford,et al.  Numerical Solution of the Bagley-Torvik Equation , 2002, BIT Numerical Mathematics.

[21]  Mohsen Razzaghi,et al.  THE LEGENDRE WAVELETS OPERATIONAL MATRIX OF INTEGRATION , 2001 .

[22]  E. A. Rawashdeh,et al.  Numerical solution of fractional integro-differential equations by collocation method , 2006, Appl. Math. Comput..

[23]  Eid H. Doha,et al.  A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order , 2011, Comput. Math. Appl..

[24]  Muhammad Aslam Noor,et al.  Numerical methods for fourth-order fractional integro-differential equations , 2006, Appl. Math. Comput..

[25]  Esmail Babolian,et al.  Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration , 2007, Appl. Math. Comput..

[26]  Li Huang,et al.  Approximate solution of fractional integro-differential equations by Taylor expansion method , 2011, Comput. Math. Appl..

[27]  Parviz Darania,et al.  A method for the numerical solution of the integro-differential equations , 2007, Appl. Math. Comput..

[28]  S. Momani,et al.  Numerical comparison of methods for solving linear differential equations of fractional order , 2007 .

[29]  S. Shahmorad,et al.  Numerical solution of a class of Integro-Differential equations by the Tau Method with an error estimation , 2003, Appl. Math. Comput..