Numerical study of nonlinear time-fractional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising in propagation of waves

Anjali Rao, Ramesh Kumar Vats and Sanjeev Yadav

Chaos, Solitons & Fractals, 2024, vol. 184, issue C

Abstract: In this manuscript, the numerical approximation of the solution for time-fractional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) nonlinear partial differential equation is described involving the Caputo fractional derivative with the help of two novel techniques namely, Sumudu Residual Power Series (SRPS) method and Homotopy Perturbation Sumudu Transform (HPST) method. CDGSK equation describe the propagation of capillary waves and shallow water waves. The results obtained through numerical approximation shows that both SRPS and HPST under consideration are reliable and efficient. The present framework precisely reflects the behavior of the obtained result for various fractional orders. Additionally, we conduct a comparison between the exact solution and an approximate series solution to affirm the efficacy of the proposed techniques. This analysis highlights the efficiency and precision of both techniques in solving nonlinear fractional differential equations. All the numerical simulations are demonstrated graphically using Maple and Matlab.

Keywords: Fractional differential equation; Caudrey–Dodd–Gibbon–Sawada–Kotera equation; Sumudu residual power series method; Approximate solution; Homotopy perturbation Sumudu transform method; Caputo fractional derivative (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924004934

DOI: 10.1016/j.chaos.2024.114941

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