(4)An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves
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Ved Prakash Dubeya, Rajnesh Kumarb, Jagdev Singhc, Devendra Kumard,∗
aFaculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Lucknow- Deva Road, Uttar Pradesh-225003, India
b Department of Applied Science and Humanities, Government Engineering College, Nawada, Department of Science and Technology, Bihar-805122, India
c Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India
d Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
Received 29 January 2020; received in revised form 25 April 2020; accepted 25 April 2020
Available online 23 May 2020
Abstract
In this paper, an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu
transform is applied to investigate the time-fractional modified Degasperis-Procesi (DP) equation. The present study considers the Caputo
fractional derivative. The fractional order modified DP model is very important and plays a great role in study of ocean engineering and
science. The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter and the asymptotic parameter
ρ ( ≥ 1) to handle mainly the differential equations of nonlinear nature. The offered scheme produces the solution in the shape of a convergent
series in a large admissible domain which is helpful to regulate the region of convergence of a series solution. The proposed work computes
the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the
obtained solution for diverse values of the fractional parameter β.
© 2020 Published by Elsevier B.V. on behalf of Shanghai Jiaotong University.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Fractional Degasperis-Procesi equation; Nonlinear dispersive waves; Analytical solution; q-homotopy analysis method; Sumudu transform.