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Solution of Time-Fractional Rosenau-Hyman Model Using a Robust Homotopy Approach via Formable Transform

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Abstract

This work considers a robust homotopy analysis method with a formable transform that investigates a time-fractional Rosenau-Hyman model based on a KdV-like equation having compacton solutions. Here, a novel technique that combines the homotopy analysis method with formable transformation has been implemented, called \(\eta\)-homotopy analysis formable transformation technique (\(\eta\)-HAFTT) to obtain an approximate analytical solution of the time-fractional Rosenau-Hyman equation. Finally, the \(\eta\)-HAFTT solution is compared with the available solution numerically and graphically to check the efficacy of the obtained solution. It shows that the new suggested algorithm (\(\eta\)-HAFTT) provides the approximate solutions with the least approximations having better accuracy.

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  1. Department of Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, 395007, Surat, Gujarat, India

    Vishalkumar J. Prajapati & Ramakanta Meher

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  1. Vishalkumar J. Prajapati
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  2. Ramakanta Meher
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Correspondence to Ramakanta Meher.

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Prajapati, V.J., Meher, R. Solution of Time-Fractional Rosenau-Hyman Model Using a Robust Homotopy Approach via Formable Transform. Iran J Sci Technol Trans Sci 46, 1431–1444 (2022). https://doi.org/10.1007/s40995-022-01347-w

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  • DOI: https://doi.org/10.1007/s40995-022-01347-w

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