Numerical studies for a multi-order fractional differential equation

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 371, Issue 1-2, 2007, Pages 26-33

  Sweilam, N H ^a   Khader, M M ^b   Al Bar, R F ^c  

^a CAIRO UNIVERSITY   (Egypt)

^b BENHA UNIVERSITY   (Egypt)

^c UMM AL QURA UNIVERSITY   (Saudi Arabia)

Author keywords

Caputo fractional derivative; Fractional differential equation; Homotopy perturbation method; Lagrange multiplier; Variational iteration method

Indexed keywords

DIFFERENTIATION (CALCULUS); LAGRANGE MULTIPLIERS; PERTURBATION TECHNIQUES;

CAPUTO FRACTIONAL DERIVATIVES; COMPUTABLE COMPONENTS; CONVERGENT SERIES; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; HOMOTOPY PERTURBATION METHOD (HPM); NUMERICAL RESULTS; VARIATIONAL ITERATION METHOD;

ITERATIVE METHODS;

EID: 35349007940     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2007.06.016     Document Type: Article

References (27)

1. Abdou M.A., and Soliman A.A. Physica D 211 (2005) 1
2. Abdou M.A., and Soliman A.A. J. Comput. Appl. Math. (2004) 1
3. Bagley R.L., and Calico R.A. J. Guidance Control Dynamics 14 2 (1999)
4. Benson D.A., Wheatcraft S.W., and Meerschaert M.M. Water Resour. Res. 36 6 (2000) 1403
5. Benson D.A., Wheatcraft S.W., and Meerschaert M.M. Water Resour. Res. 36 6 (2000) 1413
6. Daftardar-Gejji V., and Jafari H. Appl. Math. Comput. 189 1 (2007) 541
7. Diethelm K., and Ford N.J. Appl. Math. Comput. 154 (2004) 621
8. Djrbashian M.M., and Nersesian A.B. Izv. Acad. Nauk Armjanskoy SSR 3 1 (1968) 3 (in Russian)
9. He J.H. Int. J. Mod. Phys. B 20 10 (2006) 1141
10. He J.H. Int. J. Non-Linear Mech. 34 (1999) 699
11. He J.H., and Wu X.-H. Chaos Solitons Fractals 29 (2006) 108
12. Huang F., and Liu F. ANZIAM J. 46 (2005) 317
13. Ichise M., Nagayanagi Y., and Kojima T. J. Electroanal. Chem. Interfacial Electrochem. 33 (1971) 253
14. Kilbas A.A., Saigo M., and Saxena R.K. J. Integral Equations Appl. 14 4 (2002) 377
15. Koeller R.C. Acta Mech. 58 (1984) 299
16. Koeller R.C. J. Appl. Mech. 51 (1984) 299
17. Liu F., Anh V., Turner I., and Zhuang P. J. Appl. Math. Comput. (2003) 233
18. Mandelbrot B. IEEE Trans. Inform. Theory 13 2 (1967) 289
19. Mark R.J., and Hall M.W. IEEE Trans. Acoust. Speech Signal Process. 29 (1981) 872
20. Miller K.S., and Boss B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley, New York
21. Oldham K.B., and Spanier J.C. The Fractional Calculus (1974), Academic Press, San Diego, CA
22. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego, CA
23. Skaar S.B., Michel A.N., and Miller R.K. IEEE Trans. Automat. Control 3 4 (1988) 348
24. Sweilam N.H., and Khader M.M. Chaos Solitons Fractals 32 (2007) 145
25. Sweilam N.H. J. Comput. Appl. Math. 207 (2007) 64
26. Sun H.H., Onaral N., and Tsao Y. IEEE Trans. Ciomed. Eng. 31 10 (1984) 664
27. Sun H.H., Abdelwahab A.A., and Onaral B. IEEE Trans. Automat. Control 29 5 (1984) 441