Abstract
In this paper, the homotopy perturbation method is adopted to find explicit and numerical solutions for systems of non-linear fractional shallow water equations. The fractional derivatives are described in the Caputo sense. We apply both the homotopy perturbation method and the homotopy analysis method, to solve certain shallow water equations with time-fractional derivatives, and explicitly construct convergent power series solutions. The results obtained reveal that these methods are both very effective and simple for finding approximate solutions. Some numerical examples and plots are presented to illustrate the efficiency and reliability of these methods.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol19iss1pp74-86
- Journal
- Sultan Qaboos University Journal for Science, 19(1), 74
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Al‐Khaled, K., & Al-Safeen, M. K. (2014). Homotopy Perturbation Method For Fractional Shallow Water Equations. Sultan Qaboos University Journal for Science, 19(1), 74. https://doi.org/10.24200/squjs.vol19iss1pp74-86
MLA 9
Al‐Khaled, Kamel, and M. K. Al-Safeen. "Homotopy Perturbation Method For Fractional Shallow Water Equations." Sultan Qaboos University Journal for Science, vol. 19, no. 1, 2014, pp. 74. https://doi.org/10.24200/squjs.vol19iss1pp74-86.
Chicago (author–date)
Al‐Khaled, Kamel, and M. K. Al-Safeen. 2014. "Homotopy Perturbation Method For Fractional Shallow Water Equations." Sultan Qaboos University Journal for Science 19 (1): 74. https://doi.org/10.24200/squjs.vol19iss1pp74-86.
Harvard
Al‐Khaled, K. and Al-Safeen, M. K. (2014) 'Homotopy Perturbation Method For Fractional Shallow Water Equations', Sultan Qaboos University Journal for Science, 19(1), pp. 74. doi:10.24200/squjs.vol19iss1pp74-86.
Vancouver
Al‐Khaled K, Al-Safeen MK. Homotopy Perturbation Method For Fractional Shallow Water Equations. Sultan Qaboos University Journal for Science. 2014;19(1):74. doi:10.24200/squjs.vol19iss1pp74-86
IEEE
K. Al‐Khaled, and M. K. Al-Safeen, "Homotopy Perturbation Method For Fractional Shallow Water Equations," Sultan Qaboos University Journal for Science, vol. 19, no. 1, pp. 74, 2014, doi: 10.24200/squjs.vol19iss1pp74-86.