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Constructing the fractional series solutions for time-fractional K-dV equation using Laplace residual power series technique

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Abstract

In this article, we construct the series solution of the time-fractional Korteveg de Vries (K-dV) equation through a computational approach named as Laplace residual power series (LRPS) that combines the Laplace transform with the residual power series method (RPS). Time-fractional K-dV equation is used to modeled various real life phenomena like propagation of waves in elastic rods, dispersion effects in shallow coastal regions, anomalous diffusion observed in financial markets. The Caputo fractional derivative is used in the formulation of time-fractional K-dV equation. LRPS method is characterized by its rapid convergence and easy finding of the unknown coefficients using the concept of limit at infinity without any perturbation, discretization and linearization. To assess the effectiveness of proposed computational strategy, we perform a comparative analysis among the fractional residual power series method, the Adomian decomposition method, and the RPS method. Additionally, we examine the convergence of the fractional series solution across different \(\alpha \) values and assess the solution’s behavior as the time domain increased. The efficiency and authenticity of the LRPS method is shown by computing the absolute error, relative error and residual error. This work is supported by 2D and 3D graphical representations made in accordance with Maple and MATLAB.

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Acknowledgements

First author grateful to U.G.C. for providing fellowship to carry his research work. The authors would like to thank the anonymous referees for their insightful remarks and ideas to improve the article’s quality.

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The authors declare that they did not receive any funds, grants, or other support during the preparation of this manuscript.

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  1. Department of Mathematics and Scientific Computing, National Institute of Technology Hamirpur, Hamirpur, Himachal Pradesh, 177005, India

    Sanjeev Yadav, Ramesh Kumar Vats & Anjali Rao

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  1. Sanjeev Yadav
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  2. Ramesh Kumar Vats
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  3. Anjali Rao
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SY: Conceptualization, Writing—Original draft, Methodology, Software, Data curation. RKV: Supervision, Validation. AR: Editing & Review, Visualization.

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Correspondence to Anjali Rao.

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Yadav, S., Vats, R.K. & Rao, A. Constructing the fractional series solutions for time-fractional K-dV equation using Laplace residual power series technique. Opt Quant Electron 56, 721 (2024). https://doi.org/10.1007/s11082-024-06412-9

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