Analytical approach to linear fractional partial differential equations arising in fluid mechanics

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

Volumn 355, Issue 4-5, 2006, Pages 271-279

  Momani, Shaher ^a   Odibat, Zaid ^b  

^a MUTAH UNIVERSITY   (Jordan)

^b AL BALQA APPLIED UNIVERSITY   (Jordan)

Author keywords

Caputo derivative; Decomposition method; Fluid mechanics; Fractional differential equations; Variational iteration method

Indexed keywords

FLUID MECHANICS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; VARIATIONAL TECHNIQUES;

ADOMIAN DECOMPOSITION METHOD; CAPUTO DERIVATIVES; DECOMPOSITION METHODS; EFFICIENCY AND RELIABILITY; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL ORDER EQUATIONS; FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS; VARIATIONAL ITERATION METHOD;

ITERATIVE METHODS;

EID: 33646878106     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2006.02.048     Document Type: Article

References (41)

1. J.H. He, Nonlinear oscillation with fractional derivative and its applications, International Conference on Vibrating Engineering'98, Dalian, China, 1998, pp. 288-291
2. He J.H. Bull. Sci. Technol. 15 2 (1999) 86
3. He J.H. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57
4. Mainardi F. Fractional calculus: Some basic problems in continuum and statistical mechanics. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer-Verlag, New York 291-348
5. Podlubny I. Fractional Differential Equations (1999), Academic Press, New York
6. He J.H. Commun. Nonlin. Sci. Numer. Simulation 2 4 (1997) 235
7. He J.H. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57
8. He J.H. Comput. Methods Appl. Mech. Engrg. 167 (1998) 69
9. He J.H. Int. J. Nonlinear Mech. 34 (1999) 699
10. He J.H. Appl. Math. Comput. 114 (2000) 115
11. He J.H., Wan Y.Q., and Guo Q. Int. J. Circuit Theor. Appl. 32 6 (2004) 629
12. Adomian G. J. Math. Anal. Appl. 135 (1988) 501
13. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers, Boston
14. Shawagfeh N., and Kaya D. Appl. Math. Lett. 17 (2004) 323
15. Momani S. Math. Comput. Simulation 70 2 (2005) 110
16. Momani S. Chaos Solitons Fractals 28 4 (2006) 930
17. S. Momani, Z. Odibat, Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method, Appl. Math. Comput., in press
18. S.S. Ray, R.K. Bera, Analytical solution of a fractional diffusion equation by Adomian decomposition method, Appl. Math. Comput. in press
19. Marinca V. Int. J. Nonlin. Sci. Numer. Simulation 3 2 (2002) 107
20. Drǎgǎnescu G.E., and Cǎpǎlnǎsan V. Int. J. Nonlin. Sci. Numer. Simulation 4 3 (2003) 219
21. Liu H.M. Chaos Solitons Fractals 23 2 (2005) 573
22. Hao T.H. Int. J. Nonlin. Sci. Numer. Simulation 6 2 (2005) 209
23. Momani S., and Abuasad S. Chaos Solitons Fractals 27 5 (2006) 1119
24. Odibat Z., and Momani S. Int. J. Nonlin. Sci. Numer. Simulation 7 1 (2006) 27
25. Debnath L., and Bhatta D. Fract. Calc. Appl. Anal. 7 (2004) 21
26. Diethelm K., Ford J.M., Ford N.J., and Weilbeer M. J. Comput. Appl. Math. 186 (2006) 482
27. Gorenflo R. Afterthoughts on interpretation of fractional derivatives and integrals. In: Rusev P., Dimovski I., and Kiryakova V. (Eds). Transform Methods and Special Functions, Varna 96 (1998), Bulgarian Academy of Sciences, Institute of Mathematics ands Informatics, Sofia 589-591
28. A. Luchko, R. Gorenflo, The initial value problem for some fractional differential equations with the Caputo derivative, preprint series A08-98, Fachbreich Mathematik und Informatik, Freic Universitat Berlin, 1998
29. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), John Wiley and Sons, New York
30. Oldham K.B., and Spanier J. The Fractional Calculus (1974), Academic Press, New York
31. Caputo M. J. Roy. Astron. Soc. 13 (1967) 529
32. Podlubny I. Fract. Calc. Appl. Anal. 5 (2002) 367
33. Inokuti M., Sekine H., and Mura T. General use of the Lagrange multiplier in non-linear mathematical physics. In: Nemat-Nasser S. (Ed). Variational Method in the Mechanics of Solids (1978), Pergamon Press, Oxford 156-162
34. He J.H. Int. J. Turbo Jet-Engines 14 1 (1997) 23
35. He J.H. Int. J. Nonlin. Sci. Numer. Simulation 2 4 (2001) 309
36. He J.H. Generalized Variational Principles in Fluids (2003), Science and Culture Publishing House of China, Hong Kong pp. 222-230 (in Chinese)
37. He J.H. Int. J. Nonlin. Sci. Numer. Simulation 4 3 (2003) 313
38. He J.H. Chaos Solitons Fractals 19 4 (2004) 847
39. Liu H.M. Int. J. Nonlin. Sci. Numer. Simulation 5 1 (2004) 95
40. Cherruault Y. Kybernetes 18 (1989) 31
41. Cherruault Y., and Adomian G. Math. Comput. Modelling 18 (1993) 103