Homotopy analysis method for solving biological population model

Communications in Theoretical Physics

Volumn 56, Issue 5, 2011, Pages 797-800

  Arafa, A A M ^a   Rida, S Z ^a   Mohamed, H ^b  

^a SOUTH VALLEY UNIVERSITY   (Egypt)

^b ASWAN UNIVERSITY   (Egypt)

Author keywords

biological populations model; fractional calculus; homotopy analysis method; MittagLeffler function

Indexed keywords

EID: 81555196325     PISSN: 02536102     EISSN: None     Source Type: Journal    
DOI: 10.1088/0253-6102/56/5/01     Document Type: Article

References (32)

1. S.Z. Rida, A.M.A. El-Sayed and A.A.M. Arafa 2010 J. Statistical Phys. 140 797
2. A.M.A. El-Sayed, S.Z. Rida and A.A.M. Arafa 2010 Acta Appl. Math. 110 1501
3. S.Z. Rida, A.M.A. El-Sayed, A.A.M. Arafa 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3847
4. S.Z. Rida, A.M.A. El-Sayed and A.A.M. Arafa 2010 Nonlinear Sci. Lett. A 1 415
5. A.M.A. El-Sayed, S.Z. Rida and A.A.M. Arafa 2010 Int. J. Math. Modeling, Simulation Appl. 3 231
6. A.M.A. El-Sayed, S.Z. Rida and A.A.M. Arafa 2009 Commun. Theor. Phys. 52 992
7. A.M.A. El-Sayed, S.Z. Rida and A.A.M. Arafa 2009 Int. J. Nonlinear Sci. 7 485
8. S.Z. Rida, H.M. El-Sherbiny and A.A.M. Arafa 2008 Phys. Lett. A 372 553
9. Y.I. Babenko 1986 Heat and Mass Transfer (Chemia, Leningrad)
10. M. Caputo and F. Mainardi 1971 Riv. Nuovo Cimento (Ser II) 1 161
11. R. Gorenflo and F. Mainardi 1997 Fractional Calculus: Integral and Differential Equations of Fractional Order Fractals Fractional Calculus in Continuum Mechanics eds. A. Carpinteri and F. Mainar (Springer Verlag, Wien and New York) p 223-276
12. R. Gorenflo and R. Rutman 1995 On Ultraslow and Intermediate Processes, in Transform Methods and Special Functions eds. P. Rusev, I. Dimovski, and V. Kiryakova (Science Culture Technology Publishing (SCTP), Singapore) p 61-81
13. F. Mainardi 1994 Fractional Relaxation and Fractional Diffusion Equations, Mathematical Aspects, in Proc. 12-th IMACS World Congress vol 1 ed. W.F. Ames p 329 Georgia Tech Atlanta
14. F. Mainardi 1997 Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics Fractals and Fractional Calculus in Continuum Mechanics eds. A. Carpinteri and F. Mainardi (Springer Verlag, Wien and New York) p 291-348
15. S. Momani 2006 Chaos, Solitons Fractals 28 930
16. S. Momani and Z. Odibat 2006 Appl. Math. Comput. 177 488
17. Z. Odibat and S. Momani 2006 Appl. Math. Comput. 181 1351
18. S. Momani 2005 Math. Comput. Simul. 70 110
19. S. Momani and Z. Odibat 2006 Phys. Lett. A 355 271
20. S. Momani and Z. Odibat 2007 Chaos, Solitons Fractals 31 1248
21. J.H. He 1998 Comput. Methods Appl. Mech. Engrg. 167 57
22. Z. Odibat and S. Momani 2006 Int. J. Nonlinear Sci. Numer. Simul. 7 15
23. Z. Odibat and S. Momani 2008 Chaos, Solitons Fractals 36 167
24. S. Momani and Z. Odibat 2007 Comput. Math. Appl. 54 910
25. S.J. Liao 1992 The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems PhD Thesis (Shanghai Jiao Tong University, Shanghai)
26. S.J. Liao and A. Campo 2002 J. Fluid. Mech. 453 411
27. M. Ayub, A. Rasheed and T. Hayat 2003 Int. J. Eng. Sci. 41 2091
28. S. Abbasbandy 2007 Int. Commum. Heat. Mass. Transfer. 34 380
29. S. Abbasbandy 2007 Phys. Lett. A 361 478
30. S. Abbasbandy 2007 Chem. Eng. J.
31. I. Podlubny 1999 Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications (Academic Press, New York)
32. M.A. Golberg 1999 Appl. Math. Comput. 106 215