Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation

References

• Abbaoui , K. and Cherruault , Y. 1995 . New ideas for proving convergence of decomposition methods . Comput. Math. Appl. , 29 : 103 – 108 .
   Web of Science ®Google Scholar
• Das , S. 2008 . Solution of fractional vibration equation by the variational iteration method and modified decomposition method . Int. J. Nonlinear Sci. Numer. Simul. , 9 : 361 – 366 .
   Web of Science ®Google Scholar
• Das , S. 2009 . A numerical solution of vibration equation using modified decomposition method . J. Sound Vib. , 320 : 576 – 583 .
   Web of Science ®Google Scholar
• El-Shahed , M. 2005 . Application of He's homotopy perturbation method to Volterra's integro-differential equation . Int. J. Nonlinear Sci. Numer. Simul. , 6 : 163 – 168 .
   Web of Science ®Google Scholar
• Hayat , T. , Khan , M. and Ayub , M. 2004 . On the explicit analytic solutions of an Oldroyd 6-constant fluid . Int. J. Eng. Sci. , 42 : 123 – 135 .
   Web of Science ®Google Scholar
• Hayat , T. , Khan , M. and Asghar , S. 2004 . Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid . Acta Mech. , 168 : 213 – 232 .
   Web of Science ®Google Scholar
• Hayat , T. , Khan , M. and Asghar , S. 2004 . Magnetohydrodynamic flow of an Oldroyd 6-constant fluid . Appl. Math. Comput. , 155 : 417 – 425 .
   Web of Science ®Google Scholar
• He , J. H. 1999 . Homotopy perturbation technique . Comput. Methods Appl. Mech. Eng. , 178 : 257 – 262 .
   Web of Science ®Google Scholar
• He , J. H. 2000 . A coupling method of homotopy technique and perturbation technique for non-linear problems . Int. J. Nonlinear Mech. , 35 : 37 – 43 .
   Web of Science ®Google Scholar
• He , J. H. 2005 . Periodic solutions and bifurcations of delay-differential equations . Phys. Lett. A , 347 : 228 – 230 .
   Web of Science ®Google Scholar
• He , J. H. 2005 . Application of homotopy perturbation method to nonlinear wave equations . Chaos Solitons Fractals , 26 : 695 – 700 .
   Web of Science ®Google Scholar
• He , J. H. 2005 . Limit cycle and bifurcation of nonlinear problems . Chaos Solitons Fractals , 26 : 827 – 833 .
   Web of Science ®Google Scholar
• He , J. H. 2005 . Homotopy perturbation method for bifurcation of nonlinear problems . Int. J. Nonlinear Sci. Numer. Simul. , 6 : 207 – 208 .
   Web of Science ®Google Scholar
• He , J. H. 2006 . Homotopy perturbation method for solving boundary value problems . Phys. Lett. A , 350 : 87 – 88 .
   Web of Science ®Google Scholar
• Liao , S. J. 1992 . “ On the proposed homotopy analysis technique for nonlinear problems and its applications ” . Shanghai : Shanghai Jiao Tong University . Ph.D. diss
   Google Scholar
• Liao , S. J. 1998 . Homotopy analysis method: A new analytic method for nonlinear problems . Appl. Math. Mech. , 19 : 957 – 962 .
   Web of Science ®Google Scholar
• Liao , S. J. 2003 . Beyond Perturbation: Introduction to the Homotopy Analysis Method , Boca Raton : CRC Press, Chapman and Hall .
   Google Scholar
• Liao , S. J. 2005 . Comparison between the homotopy analysis method and homotopy perturbation method . Appl. Math. Comput. , 169 : 1186 – 1194 .
   Web of Science ®Google Scholar
• Liao , S. J. 2006 . An analytical solution of unsteady boundary layer flows caused by an impulsively stretching plate, Commun . Nonlinear Sci. Numer. Simul. , 11 : 326 – 339 .
   Google Scholar
• Mandelbrot , B. B. and Willis , J. R. 1969 . Robustness of the rescaled range and the measurement of the long run statistical dependence . Water Resour. Res. , 5 : 967 – 988 .
   Web of Science ®Google Scholar
• Momani , S. and Odibat , Z. 2007 . Comparison between the HPM and the VIM for linear fractional partial differential equations . Comput. Math. Appl. , 54 : 910 – 919 .
   Web of Science ®Google Scholar
• Siddiqui , A. M. , Mahmood , R. and Ghori , Q. K. 2006 . Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method . Int. J. Nonlinear Sci. Numer. Simul. , 7 : 7 – 14 .
   Web of Science ®Google Scholar
• Siddiqui , A. M. , Mahmood , R. and Ghori , Q. K. 2006 . Couette and Poiseuille flows for non-Newtonian fluids . Int. J. Nonlinear Sci. Numer. Simul. , 7 : 15 – 26 .
   Web of Science ®Google Scholar
• Wu , W. and Liao , S. J. 2004 . Solving solitary waves with discontinuity by means of the homotopy analysis method . Chaos Solitons Fractals , 23 : 1733 – 1740 .
   Google Scholar