Computational analysis of fractional Drinfeld-Sokolov-Wilson equation associated with regularized form of Hilfer-Prabhakar derivative

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Abstract

In this research paper, we utilize an analytical technique to investigate the behavior of the Drinfeld-Sokolov-Wilson equation of arbitrary order. The implemented technique is an adequate composition of the Kharrat-Toma transform and the q-homotopy analysis approach. Here, a regularized form of the Hilfer-Prabhakar derivative of arbitrary order is used to formulate the problem. The Drinfeld-Sokolov-Wilson equation of arbitrary order is utilized to model the dispersive water waves and plays a very significant role in fluid dynamics. The results of the discussed model are presented graphically to show the efficiency and reliability of the obtained results.

Keywords

Prabhakar fractional calculus / regularized version of Hilfer-Prabhakar fractional derivative / Drinfeld-Sokolov-Wilson equation / Kharrat-Toma transform

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