(5)Numerical study of fractional model of multi-dimensional dispersive partial differential equation
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Vijay Verma a, Amit Prakash b, Devendra Kumar c,*, Jagdev Singh d
a Department of Mathematics, Pt. C. L. S. Govt. (PG) College, Karnal, Haryana, India
b Department of Mathematics, National Institute of Technology, Kurukshetra 136119, India
c Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
d Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
Received 23 April 2019; received in revised form 1 June 2019; accepted 2 June 2019
Available online 13 June 2019
Abstract
This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multi- dimensional space. The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering. The numerical technique comprises of Sumudu transform, homotopy perturbation scheme and He’s polynomial, namely homotopy perturbation Sumudu transform method (HPSTM) is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space. The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method. The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations. Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.
© 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: Homotopy perturbation method; Fractional trigonometric function; He’s polynomials; Adomian decomposition method; Sumudu transform.