(6)Solution for fractional potential KdV and Benjamin equations using the novel technique
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P. Veeresha a, D.G. Prakasha b,∗, N. Magesh c, A. John Christopher c, Deepak Umrao Sarwe d
a Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, India
b Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere-577007, India
cP. G. and Research Department of Mathematics, Govt. Arts College for Men, Krishnagiri - 635 001, India
d Department of Mathematics, University of Mumbai, Kalina, Santacruz East, Mumbai-400098, India
Received 21 June 2020; received in revised form 8 January 2021; accepted 26 January 2021
Available online 28 January 2021
Abstract
In this paper, we find the solutions for fractional potential Korteweg–de Vries (p-KdV) and Benjamin equations using q-homotopy analysis
transform method (q-HATM). The considered method is the mixture of q-homotopy analysis method and Laplace transform, and the Caputo
fractional operator is considered in the present investigation. The projected solution procedure manipulates and controls the obtained results
in a large admissible domain. Further, it offers a simple algorithm to adjust the convergence province of the obtained solution. To validate the
q-HATM is accurate and reliable, the numerical simulations have been conducted for both equations and the outcomes are revealed through
the plots and tables. Comparison between the obtained solutions with the exact solutions exhibits that, the considered method is efficient and
effective in solving nonlinear problems associated with science and technology.
© 2021 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: Potential KdV equation; q-Homotopy analysis method; Fractional Benjamin equation; Laplace transform; Ginzburg–Landau equation; Caputo
fractional operator.