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Volume 3, Issue 6
Homotopy Perturbation Method for Time-Fractional Shock Wave Equation

Mithilesh Singh & Praveen Kumar Gupta

DOI: 10.4208/aamm.10-m1137

Adv. Appl. Math. Mech., 3 (2011), pp. 774-783.

Published online: 2011-03

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  • Abstract

A scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method (HPM). The fractional derivatives are taken in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical results are illustrated through the graph.

  • Keywords

Partial differential equation, fractional derivative, shock wave equation, homotopy perturbation method.

  • AMS Subject Headings

76L99, 76K99, 35L10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-3-774, author = {Singh , Mithilesh and Gupta , Praveen Kumar}, title = {Homotopy Perturbation Method for Time-Fractional Shock Wave Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {6}, pages = {774--783}, abstract = {

A scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method (HPM). The fractional derivatives are taken in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical results are illustrated through the graph.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1137}, url = {http://global-sci.org/intro/article_detail/aamm/196.html} }
TY - JOUR T1 - Homotopy Perturbation Method for Time-Fractional Shock Wave Equation AU - Singh , Mithilesh AU - Gupta , Praveen Kumar JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 774 EP - 783 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1137 UR - https://global-sci.org/intro/article_detail/aamm/196.html KW - Partial differential equation, fractional derivative, shock wave equation, homotopy perturbation method. AB -

A scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method (HPM). The fractional derivatives are taken in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical results are illustrated through the graph.

Singh , Mithilesh and Gupta , Praveen Kumar. (2011). Homotopy Perturbation Method for Time-Fractional Shock Wave Equation. Advances in Applied Mathematics and Mechanics. 3 (6). 774-783. doi:10.4208/aamm.10-m1137
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