The Numerical Solution of Fractional Differential Algebraic Equations (FDAEs)

Abstract

In this paper, numerical solution of Fractional Differential–Algebraic Equations (FDAEs) is studied. Firstly Fractional Differential–Algebraic Equations (FDAEs) have been converted to power series and then numerical solution of Fractional Differential–Algebraic Equations (FDAEs) is obtained

Keywords

• Differential-Algebraic Equations (DAEs),Fractional Differential-Algebraic Equation (FDAEs),Power Series

The Numerical Solution of Fractional Differential-Algebraic Equations (FDAEs)

Öz

References

1. B. İbiş, M. Bayram, Numerical comparison of methods for solving fractional differential–algebraic equations (FDAEs), Computers & Mathematics with Applications, Volume 62, Issue 8, October 2011, Pages 3270–3278
2. E. Çelik and M. Bayram, On the Numerical Solution of Differential-Algebraic Equation by Padé Series, Applied Mathematics and Computation, 137(2003) 151-160.
3. E. Çelik, E. Karaduman and M. Bayram, A Numerical Method to Solve Chemical Differential-Algebraic Equations, International Journal of Quantum Chemistry, 89(2002) 447-451.
4. I. Podlubny, Fractional Differential Equations. An Introduction to Fractional Derivatives Fractional Differential Equations Some Methods of their Solution and Some of their Applications, Academic Press, San Diego, 1999.
5. J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Energy. 167 (1998) 57-68.
6. K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
7. K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons Inc., New York, 19 L. R. Petzold, Recent developments in the numerical solution of differential/algebraic systems, Computer Methods in Applied M echanics and Engineering, Volume 75, Issues 1–3, October 1989, Pages 77–89
8. M. Bayram and E. Çelik, (2004). Chebysev Approximation for Numerical Solution of Differential-Algebraic Equations(DAEs), International journal of Applied Mathematics&Statistics (IJAMAS), Dec. 29-39.

9. M. Caputo, Linear models of dissipation whose Q is almost frequency independent part II, J. Roy. Aust. Soc. 13 (1967) 529-539.
10. M. Zurigat, S. Momani, A. Alawneh, Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method, Comput. Math. Appl. 59 (3) (2010) 1227-1235.
11. N.T . Shawagfeh, Analytical approximate solutions for nonlinear fractional differential equations, Appl. Math. Comput. 131 (2002) 517-529.
12. Z. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equation of fractional order, Int. J. Nonlinear Sci. Numer. Simul. 1 (7) (2006) 15-27.