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

Mithilesh Singh & Praveen Kumar Gupta

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 = {Mithilesh Singh and Praveen Kumar Gupta}, 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 - Mithilesh Singh & Praveen Kumar Gupta 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 KW - fractional derivative KW - shock wave equation KW - 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.

Mithilesh Singh & Praveen Kumar Gupta. (1970). 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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