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Stability and numerical analysis of fractional BBM-Burger equation and fractional diffusion-wave equation with Caputo derivative

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Abstract

This paper gives a highly efficient technique to analyse the fractional BBM-Burger equation and fractional Diffusion-Wave equation. These equations are used to model various real-life phenomena like acoustic gravity waves, diffusion theory, anomalous diffusive systems, and wave propagation phenomena. A modified technique, which is the combination of the Homotopy perturbation method and Laplace transform, is used for getting the numerical solution. The Lyapunov function is used to investigate asymptotic stability, and the maximum absolute error for the proposed technique is also examined. The efficiency of the proposed technique is shown by computing the root mean square (RMS), \({L}^{2},\) and \({L}^{\infty }\) errors and comparing the results with the other techniques.

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  1. Department of Mathematics, National Institute of Technology, Kurukshetra, 136119, India

    Lalit Mohan & Amit Prakash

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  1. Lalit Mohan
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  2. Amit Prakash
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Amit Prakash, Ph.D. (Formal analysis: Equal; Funding acquisition: Equal; Project administration: Equal; Resources: Equal; Supervision: Equal; Validation: Equal; Writing – review & editing: Equal) Lalit Mohan, M.Sc. (Conceptualization: Equal; Data curation: Equal; Investigation: Equal; Methodology: Equal; Software: Equal; Visualization: Equal; Writing – original draft: Equal)

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Mohan, L., Prakash, A. Stability and numerical analysis of fractional BBM-Burger equation and fractional diffusion-wave equation with Caputo derivative. Opt Quant Electron 56, 26 (2024). https://doi.org/10.1007/s11082-023-05608-9

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