Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations

Applied Numerical Mathematics

Volumn 60, Issue 8, 2010, Pages 788-797

  El Sayed, A M A ^a   El Kalla, I L ^b   Ziada, E A A ^c  

^a Alexandria University Faculty Of Science   (Egypt)

^b Mansoura University   (Egypt)

^c Islamic University of Madinah   (Egypt)

Author keywords

Adomian method; Bagley Torvik equation; Caputo derivative; Convergence analysis; Fixed point theorem; Nonlinear fractional differential equation; Proposed numerical method

Indexed keywords

ADOMIAN METHOD; BAGLEY-TORVIK EQUATION; CAPUTO DERIVATIVES; CONVERGENCE ANALYSIS; FIXED POINT THEOREMS; FRACTIONAL DIFFERENTIAL EQUATIONS; NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION;

DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); NONLINEAR ANALYSIS; NONLINEAR EQUATIONS; NUMBER THEORY; NUMERICAL ANALYSIS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 77953168484     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2010.02.007     Document Type: Article

References (23)

1. Abbaoui K., and Cherruault Y. Convergence of Adomian's method applied to differential equations. Comput. Math. Appl. 28 (1994) 103-109
2. Adomian G. Stochastic System (1983), Academic Press
3. Adomian G. Nonlinear Stochastic Operator Equations (1986), Academic Press, San Diego
4. Adomian G. Nonlinear Stochastic Systems: Theory and Applications to Physics (1989), Kluwer
5. Adomian G., Rach R., and Mayer R. Modified decomposition. J. Appl. Math. Comput. 23 (1992) 17-23
6. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1995), Kluwer
7. Carpinteri A., and Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer Verlag pp. 223-276
8. Cherruault Y., Adomian G., Abbaoui K., and Rach R. Further remarks on convergence of decomposition method. Int. J. Bio-Med. Comput. 38 (1995) 89-93
9. Daftarder-Gejji V., and Babakhani A. Analysis of a system of fractional differential equations. J. Math. Anal. Appl. 293 (2004) 511-522
10. Diethelm K., and Ford N.J. Numerical solution of the Bagley-Torvik equation. BIT 42 (2002) 490-507
11. Diethelm K., and Ford N.J. Multi-order fractional differential equations and their numerical solution. Appl. Math. Comput. 154 (2004) 621-640
12. Diethelm K., and Luchko Y. Numerical solution of linear multi-term initial value problems of fractional order. J. Comput. Anal. Appl. (2004) 243-263
13. Diethelm K. Multi-term fractional differential equations multi-order fractional differential systems and their numerical solution. J. Europ. Syst. Autom. 42 (2008) 665-676
14. El-Sayed A.M.A., El-Mesiry E.M., and El-Saka H.A.A. Numerical solution for multi-term fractional (arbitrary) orders differential equations. Comput. Appl. Math. 23 (2004) 33-54
15. El-Kalla I.L. Error analysis of Adomian series solution to a class of nonlinear differential equations. Appl. Math. E-Notes 7 (2007) 214-221
16. El-Mesiry E.A.M., El-Sayed A.M.A., and El-Saka H.A.A. Numerical methods for multi-term fractional (arbitrary) orders differential equations. Appl. Math. Comput. 160 (2005) 683-699
17. Kilbas A.A., Srivastava H.M., and Trujillo J.J. Theory and Applications of Fractional Differential Equations (2006), Elsevier, New York
18. P Li C., and Wang Y.H. Numerical algorithm based on Adomian decomposition for fractional differential equations. Comput. Math. Appl. 57 10 (2009) 1672-1681
19. Li C.P., and Tao C.X. On the fractional Adams method. Comput. Math. Appl. 58 8 (2009) 1573-1588
20. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley-Interscience, New York
21. Podlubny I., and El-Sayed A.M.A. On Two Definitions of Fractional Calculus (1996), Slovak Academy of Science, Institute of Experimental Phys. 80-7099-252-2
22. Podlubny I. Fractional Differential Equations (1999), Academic Press, New York
23. Shawaghfeh N.T. Analytical approximate solution for nonlinear fractional differential equations. J. Appl. Math. Comput. 131 (2002) 517-529