Numerical methods for multi-term fractional (arbitrary) orders differential equations

Our main concern here is to give a numerical scheme to solve a nonlinear multi-term fractional (arbitrary) orders differential equation.

[1]  Ahmed M. A. El-Sayed,et al.  Linear differential equations of fractional orders , 1993 .

[2]  A. E. M. El-Mesiry,et al.  Numerical solution for multi-term fractional (arbitrary) orders differential equations , 2004 .

[3]  C. Lubich Discretized fractional calculus , 1986 .

[4]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[5]  K. Diethelm AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER , 1997 .

[6]  Alan D. Freed,et al.  On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity , 1999 .

[7]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[8]  M. Caputo Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

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

[10]  F. Mainardi,et al.  Fractals and fractional calculus in continuum mechanics , 1997 .

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

[12]  Ahmed M. A. El-Sayed,et al.  Nonlinear functional differential equations of arbitrary orders , 1998 .

[13]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[14]  Mariusz Ciesielski,et al.  A Numerical Method for Solution of Ordinary Differential Equations of Fractional Order , 2001, PPAM.

[15]  N. Ford,et al.  The numerical solution of linear multi-term fractional differential equations: systems of equations , 2002 .

[16]  Alan D. Freed,et al.  Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.

[17]  P. Hartman Ordinary Differential Equations , 1965 .

[18]  Kai Diethelm,et al.  Numerical solution of fractional order differential equations by extrapolation , 1997, Numerical Algorithms.

[19]  Kai Diethelm Predictor-corrector strategies for single and multi-term fractional differential equations , 2001, HERCMA.