Fractional perturbation technique of fractional differentiable functions

Romanian Reports of Physics

Volumn 57, Issue 9-10, 2012, Pages 1278-1284

  Wei, Ming Bo ^a   Zeng, De Qiang ^b  

^a SOUTHWEST UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NEIJIANG NORMAL UNIVERSITY   (China)

Author keywords

Fractal curves; Fractional differentiable functions; Perturbation technique

Indexed keywords

EID: 84872288219     PISSN: 1221146X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. K.M. Kolwankar, A. D Gangal, Local fractional Fokker-Planck equation, Phys. Rev. Lett. 80, 214-21 (1998).
2. J.H. He, Homotopy perturbation technique, Comput. Method. Appl. Mech. Eng. 178, 257-62 (1999).
3. J.H. He, Perturbation methods: Basic and Beyond. Amsterdam: Elsevier; (2006).
4. S. Moman, Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A 365, 345-50 (2007).
5. H. Jafari, S. Momani, Solving fractional diffusion and wave equations by modified homotopy perturbation method, Phys. Lett. A 370, 388-396 (2007).
6. Z.Z. Ganji, D.D. Ganji, Application of the homotopy perturbation method to coupled system of partial differential equations with time fractional derivatives, Topol Methods Nonlinear Anal. 31, 341-348 (2008).
7. A. Yildirim, Analytical approach to fractional partial differential equations in fluid mechanics by means of the homotopy perturbation method, Int. J. Numer. Method. H. 20, 186-200 (2010).
8. A.K. Golmankhaneh, D. Baleanu, Homotopy perturbation method for solving a system of Schrodinger-Korteweg-de Vries Equations, Rom. Rep. Phys. 63, 609-623 (2011).
9. A. Kadem, D. Baleanu, On fractional coupled Whitham-Broer-Kaup equations, Rom. J. Phys. 56, 629-635 (2011).
10. D. Baleanu, N.A. Ranjbar, R.S. J Sadati, et al., Lyapunov-Krasovskii Stability theorem for fractional systems with delay, Rom. J. Phys. 56, 636-643 (2011).
11. R. Eid, S.I. Mushih, D. Baleanu, et al., Fractional dimensional harmonic oscillator, Rom. J. Phys. 56, 323-331 (2011).
12. A. Kadem, D. Baleanu, Homotopy perturbation method for the coupled fractional Lotka-Volterra equations, Rom. J. Phys. 56, 332-338 (2011).
13. D. Baleanu, S.I. Muslih, E.M. Rabei et al., On fractional Hamiltonian systems possessing first-class constraints within Caputo derivatives, Rom. Rep. Phys. 63, 3-8 (2011).
14. F. Jarad, T. Abdeljawad, E. Gündoǧdu, D. Baleanu, On the Mittag-Leffler stability of q-fractional nonlinear dynamical systems, Proc. Romanian Acad. A 12, 309-314 (2011).
15. G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results, Comput. Math. Appl. 51, 1367-1376 (2006).
16. Y. Chen, Y. Yan, K.W. Zhang, On the local fractional derivative, J. Math. Anal. Appl. 362, 17-33 (2010).
17. A. Carpinteri, P. Cornetti, A fractional calculus approach to the description of stress and strain localization in fractal media, Chaos Solitons Fract. 13, 85-94 (2002).
18. G.C. Wu, New trends in variation iteration method, Commun. Frac. Calc. 2, 49-76 (2011).
19. K.M. Kolwankar, A.D. Gangal, Holder exponents of irregular signals and local fractional derivatives, Pramana-J. Phys. 48, 49-68 (1997).
20. K.M. Kolwankar, A.D. Gangal, Fractional differentiability of nowhere differentiable functions and dimensions, Chaos, 6, 505-513 (1996).
21. K.M. Kolwankar, Decomposition of Lebesgue-Cantor devil's staircase, Fractals, 12, 375-380 (2004).
22. G.C. Wu, E.W.M. Lee, Fractional variational iteration method and its application, Phys. Lett. A 374, 2506-2509 (2010).
23. Z.G. Deng, G.C. Wu, Approximate solution of fractional differential equations with uncertainty, Rom. J. Phys. 56, 868-872 (2011).
24. G.C. Wu, Adomian decomposition method for non-smooth initial value problems, Math. Comput. Model. 54, 2104-2108 (2011).
25. G.C. Wu, Y.G. Shi, K.T. Wu, Adomian decomposition method and non-analytical solution of local fractional differential equations, Rom. J. Phys. 56, 873-880 (2011).