Series solutions of time-fractional PDEs by homotopy analysis method

Differential Equations and Nonlinear Mechanics

Volumn 2008, Issue , 2008, Pages

  Hashim, I ^a   Abdulaziz, O ^a   Saif, A ^a  

^a UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59849106542     PISSN: 16874099     EISSN: 16874102     Source Type: Journal    
DOI: 10.1155/2008/686512     Document Type: Article

References (54)

1. Oldham K. B., Spanier J., The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order 1974 111 New York, NY, USA Academic Press xiii+234 Mathematics in Science and Engineering
2. Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 New York, NY, USA John Wiley Sons xvi+366 A Wiley-Interscience Publication
3. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering
4. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier North-Holland Mathematics Studies
5. Shawagfeh N. T., Analytical approximate solutions for nonlinear fractional differential equations Applied Mathematics and Computation 2002 131 2-3 517 529
6. Ray S. S., Bera R. K., Solution of an extraordinary differential equation by Adomian decomposition method Journal of Applied Mathematics 2004 2004 4 331 338
7. Ray S. S., Bera R. K., An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method Applied Mathematics and Computation 2005 167 1 561 571
8. Abdulaziz O., Hashim I., Chowdhury M. S. H., Zulkifle A. K., Assessment of decomposition method for linear and nonlinear fractional differential equations Far East Journal of Applied Mathematics 2007 28 1 95 112
9. Abdulaziz O., Hashim I., Ismail E. S., Approximate analytical solutions to fractional modified KdV equations by decomposition method Far East Journal of Applied Mathematics 2007 29 3 455 468
10. Hashim I., Selamat M. S., Simulation of time-dependent enzyme kinetics by an explicit numeric-analytic technique Far East Journal of Applied Mathematics 2008 30 1 115 124
11. Momani S., Non-perturbative analytical solutions of the space- and time-fractional Burgers equations Chaos, Solitons Fractals 2006 28 4 930 937
12. Momani S., Odibat Z., Analytical approach to linear fractional partial differential equations arising in fluid mechanics Physics Letters A 2006 355 4-5 271 279
13. Wang Q., Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method Applied Mathematics and Computation 2006 182 2 1048 1055
14. Al-Mdallal Q. M., An efficient method for solving fractional Sturm-Liouville problems. Chaos, Solitons Fractals. In press
15. He J.-H., Application of homotopy perturbation method to nonlinear wave equations Chaos, Solitons Fractals 2005 26 3 695 700
16. Odibat Z., Momani S., Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order Chaos, Solitons Fractals 2008 36 1 167 174
17. Momani S., Odibat Z., Homotopy perturbation method for nonlinear partial differential equations of fractional order Physics Letters A 2007 365 5-6 345 350
18. Wang Q., Homotopy perturbation method for fractional KdV-Burgers equation Chaos, Solitons Fractals 2008 35 5 843 850
19. Odibat Z., Exact solitary solutions for variants of the KdV equations with fractional time derivatives. Chaos, Solitons Fractals. In press
20. Odibat Z., Momani S., Application of variational iteration method to nonlinear differential equations of fractional order International Journal of Nonlinear Science and Numerical Simulation 2006 7 1 27 34
21. Momani S., Odibat Z., Numerical comparison of methods for solving linear differential equations of fractional order Chaos, Solitons Fractals 2007 31 5 1248 1255
22. He J.-H., Wu X.-H., Construction of solitary solution and compacton-like solution by variational iteration method Chaos, Solitons Fractals 2006 29 1 108 113
23. Molliq R Y., Noorani M. S. M., Hashim I., Variational iteration method for fractional heat- and wave-like equations. Nonlinear Analysis: Real World Applications. In press
24. Abbasbandy S., An approximation solution of a nonlinear equation with Riemann-Liouvilles fractional derivatives by Hes variational iteration method Journal of Computational and Applied Mathematics 2007 207 1 53 58
25. Wu X.-H., He J.-H., EXP-function method and its application to nonlinear equations Chaos, Solitons Fractals 2008 38 3 903 910
26. Liao S.-J., The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis 1992 Shanghai, China Shanghai Jiao Tong University
27. Liao S.-J., An approximate solution technique not depending on small parameters: a special example International Journal of Non-Linear Mechanics 1995 30 3 371 380
28. Liao S.-J., A kind of approximate solution technique which does not depend upon small parametersII. An application in fluid mechanics International Journal of Non-Linear Mechanics 1997 32 5 815 822
29. Liao S.-J., Beyond Perturbation: Introduction to the Homotopy Analysis Method 2004 2 Boca Raton, Fla, USA Chapman Hall/CRC xii+322 CRC Series: Modern Mechanics and Mathematics
30. Bataineh A. S., Noorani M. S. M., Hashim I., Solving systems of ODEs by homotopy analysis method Communications in Nonlinear Science and Numerical Simulation 2008 13 10 2060 2070
31. Bataineh A. S., Noorani M. S. M., Hashim I., Approximate analytical solutions of systems of PDEs by homotopy analysis method Computers Mathematics with Applications 2008 55 12 2913 2923
32. Bataineh A. S., Noorani M. S. M., Hashim I., Approximate solutions of singular two-point BVPs by modified homotopy analysis method Physics Letters A 2008 372 22 4062 4066
33. Bataineh A. S., Noorani M. S. M., Hashim I., Modified homotopy analysis method for solving systems of second-order BVPs Communications in Nonlinear Science and Numerical Simulation 2009 14 2 430 442
34. Bataineh A. S., Noorani M. S. M., Hashim I., The homotopy analysis method for Cauchy reaction-diffusion problems Physics Letters A 2008 372 5 613 618
35. Abbasbandy S., Yrsoy M., Pakdemirli M., The analysis approach of boundary layer equations of power-law fluids of second grade Zeitschrift fr Naturforschung 2008 63a 564 570
36. Abbasbandy S., Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method Applied Mathematical Modelling 2008 32 12 2706 2714
37. Hayat T., Abbas Z., Channel flow of a Maxwell fluid with chemical reaction Zeitschrift fr Angewandte Mathematik und Physik 2008 59 1 124 144
38. Hayat T., Abbas Z., Sajid M., Heat and mass transfer analysis on the flow of a second grade fluid in the presence of chemical reaction Physics Letters A 2008 372 14 2400 2408
39. Abbas Z., Hayat T., Radiation effects on MHD flow in a porous space International Journal of Heat and Mass Transfer 2008 51 5-6 1024 1033
40. Rashidi M. M., Domairry G., Dinarvand S., Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method Communications in Nonlinear Science and Numerical Simulation 2009 14 3 708 717
41. Domairry G., Fazeli M., Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity Communications in Nonlinear Science and Numerical Simulation 2009 14 2 489 499
42. Liao S.-J., Notes on the homotopy analysis method: some definitions and theorems Communications in Nonlinear Science and Numerical Simulation 2009 14 4 983 997
43. Wu Y., Cheung K. F., Explicit solution to the exact Riemann problem and application in nonlinear shallow-water equations International Journal for Numerical Methods in Fluids 2008 57 11 1649 1668
44. Song L., Zhang H., Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation Physics Letters A 2007 367 1-2 88 94
45. Cang J., Tan Y., Xu H., Liao S.-J., Series solutions of non-linear Riccati differential equations with fractional order. Chaos, Solitons Fractals. In press
46. Hashim I., Abdulaziz O., Momani S., Homotopy analysis method for fractional IVPs Communications in Nonlinear Science and Numerical Simulation 2009 14 3 674 684
47. Song L., Zhang H., Solving the fractional BBM-Burgers equation using the homotopy analysis method. Chaos, Solitons Fractals. In press
48. Bataineh A. S., Alomari A. K., Noorani M. S. M., Hashim I., Nazar R., Series solutions of systems of nonlinear fractional differential equations Acta Applicandae Mathematicae 2009 105 2 189 198
49. Xu H., Cang J., Analysis of a time fractional wave-like equation with the homotopy analysis method Physics Letters A 2008 372 8 1250 1255
50. Xu H., Liao S.-J., You X.-C., Analysis of nonlinear fractional partial differential equations with the homotopy analysis method Communications in Nonlinear Science and Numerical Simulation 2009 14 4 1152 1156
51. Jafari H., Seifi S., Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation Communications in Nonlinear Science and Numerical Simulation 2009 14 5 2006 2012
52. Jafari H., Seifi S., Solving a system of nonlinear fractional partial differential equations using homotopy analysis method Communications in Nonlinear Science and Numerical Simulation 2009 14 5 1962 1969
53. Caputo M., Linear models of dissipation whose Q is almost frequency independent-II Geophysical Journal International 1967 13 5 529 539
54. Gorenflo R., Mainardi F., Fractional calculus: integral and differential equations of fractional order Fractals and Fractional Calculus in Continuum Mechanics (Udine, 1996) 1997 378 Vienna, Austria Springer 223 276 CISM Courses and Lectures