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Optical and Quantum Electronics

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01-01-2024

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

Authors: Lalit Mohan, Amit Prakash

Published in: Optical and Quantum Electronics | Issue 1/2024

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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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Title: Stability and numerical analysis of fractional BBM-Burger equation and fractional diffusion-wave equation with Caputo derivative
Authors: Lalit Mohan
Amit Prakash
Publication date: 01-01-2024
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 1/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-05608-9

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