(2)An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma
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Amit Goswami a, Jagdev Singh b, Devendra Kumar c,∗, Sumit Gupta d, Sushila e
a Department of Physics, Jagan Nath University, Jaipur 303901, Rajasthan, India
b Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
c Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
d Department of Mathematics, Swami Keshvanand Institute of Technology, Management and Gramothan, Ramnagaria, Jaipur 302017, Rajasthan, India
e Department of Physics, Vivekananda Global University, Jaipur 303012, Rajasthan, India
Received 21 November 2018; received in revised form 22 January 2019; accepted 23 January 2019
Available online 24 January 2019
Abstract
In this work, we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method (HPSTM) to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave (RLW) equations. The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans. The derived results are very significant and imperative for explaining various physical phenomenons. The suggested method basically demonstrates how two efficient techniques, the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations. The nonlinear expressions can be simply managed by application of He’s polynomials. The result shows that the HPSTM is very powerful, efficient, and simple and it eliminates the round-off errors. It has been observed that the proposed technique can be widely employed to examine other real world problems.
© 2019 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Sumudu transform scheme; Homotopy perturbation technique; RLW equations; Ion acoustic wave; Shallow water waves in oceans.